{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "b194738b-1d0c-4884-ac46-aa1c0a45bf17",
   "metadata": {},
   "source": [
    "# Linear assignment problem\n",
    "\n",
    "The [linear assignment problem](https://en.wikipedia.org/wiki/Linear_assignment_problem) is a fundamental problem in combinatorial optimization.\n",
    "\n",
    "In this problem, we are given an $n \\times m$ cost matrix.\n",
    "The goal is to compute an assignment, i.e. a set of pairs of rows and columns, in such a way that:\n",
    "- At most one column is assigned to each row.\n",
    "- At most one row is assigned to each column.\n",
    "- The total number of assignments is $\\min(n, m)$.\n",
    "- The assignment minimizes the sum of costs.\n",
    "\n",
    "Equivalently, given a weighted complete bipartite graph, the problem is to find a maximum-cardinality matching that minimizes the sum of the weights of the edges included in the matching.\n",
    "\n",
    "Formally, the problem is as follows. Given $C \\in \\mathbb{R}^{n \\times m}$, solve the following [integer linear program](https://en.wikipedia.org/wiki/Integer_linear_program):\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "    \\text{minimize} \\quad & \\sum_{i \\in [n]} \\sum_{j \\in [m]} C_{ij} X_{ij} \\\\\n",
    "    \\text{subject to} \\quad\n",
    "    & X_{ij} \\in \\{0, 1\\} & \\forall i \\in [n], j \\in [m] \\\\\n",
    "    & \\sum_{i \\in [n]} X_{ij} \\leq 1 & \\forall j \\in [m] \\\\\n",
    "    & \\sum_{j \\in [m]} X_{ij} \\leq 1 & \\forall i \\in [n] \\\\\n",
    "    & \\sum_{i \\in [n]} \\sum_{j \\in [m]} X_{ij} = \\min(n, m)\n",
    "\\end{align*}\n",
    "$$\n",
    "\n",
    "The [Hungarian algorithm](https://en.wikipedia.org/wiki/Hungarian_algorithm) is a cubic-time algorithm for this problem."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "96410ba2-4db6-4cfa-a904-ef14b42d57a4",
   "metadata": {},
   "source": [
    "First, we install [NetworkX](https://networkx.org/), a Python library that lets us draw graphs.\n",
    "You can do this by running the following command on your terminal:\n",
    "```\n",
    "pip install -U networkx\n",
    "```\n",
    "Next, we import the libraries we will use:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "ac65e99e-9622-417a-9412-c228d9e9c8dc",
   "metadata": {},
   "outputs": [],
   "source": [
    "import networkx as nx\n",
    "from jax import random\n",
    "import optax\n",
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c9f58fb6-3174-4e10-8877-8cb6f1359d23",
   "metadata": {},
   "source": [
    "We sample a random cost matrix:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "d0caeb06-ecc1-4c9b-95e8-119fb135965b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.08482574  1.9097648   0.29561743]\n",
      " [ 1.120948    0.33432344 -0.82606775]\n",
      " [ 0.6481277  -1.0353061  -0.7824839 ]\n",
      " [-0.4539462   0.6297971   0.81524646]\n",
      " [-0.32787678 -1.1234448  -1.6607416 ]]\n"
     ]
    }
   ],
   "source": [
    "n = 5  # number of rows\n",
    "m = 3  # number of columns\n",
    "\n",
    "key = random.key(0)\n",
    "costs = random.normal(key, (n, m))\n",
    "print(costs)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3d04a574-e65c-481d-b1df-54c75ae85c43",
   "metadata": {},
   "source": [
    "We can visualize the cost matrix as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "d90d7969-5ab0-4c49-ab96-3d5a96aa53a5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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7tJbxY69PRNRffPHFskcrZEn/HQIw15K9hwD8kCAASRCAJAhAEgQgCQKQBAFIggAkQQCSIABJEIAkCED6H3ZUz92KVvJ7AAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(costs, cmap=\"gray\");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6d877fa6-f667-4120-a9a7-630a530e0c62",
   "metadata": {},
   "source": [
    "We can also visualize the costs as a weighted bipartite graph. Below, rows are shown as nodes the left and columns are shown as nodes the right."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "101a7e92-0aaa-4c29-9e2f-ee21bfceadba",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "G = nx.Graph()\n",
    "rows = [f\"row {i}\" for i in range(n)]\n",
    "cols = [f\"col {j}\" for j in range(m)]\n",
    "edges = [(rows[i], cols[j], {\"cost\": costs[i, j]}) for i in range(n) for j in range(m)]\n",
    "G.add_nodes_from(rows + cols)\n",
    "G.add_edges_from(edges)\n",
    "layout = nx.bipartite_layout(G, rows)\n",
    "nx.draw(G, layout)\n",
    "nx.draw_networkx_edge_labels(\n",
    "    G,\n",
    "    layout,\n",
    "    edge_labels={(u, v): f\"{info[\"cost\"]:g}\" for u, v, info in edges},\n",
    "    rotate=False,\n",
    "    font_size=8,\n",
    "    bbox=dict(\n",
    "        pad=0.0,\n",
    "        facecolor=\"white\",\n",
    "        edgecolor=\"none\",\n",
    "    ),\n",
    ");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f0db2563-131f-4f5d-8bbd-91e49c6457f9",
   "metadata": {},
   "source": [
    "To solve the problem, we call {py:func}`optax.assignment.hungarian_algorithm` on the cost matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "f591ac88-a926-4223-89e7-1569fcfcfbf9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2 3 4] [1 0 2]\n"
     ]
    }
   ],
   "source": [
    "sol_i, sol_j = optax.assignment.hungarian_algorithm(costs)\n",
    "print(sol_i, sol_j)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "365f3f02-7430-4225-906a-05f912b2d0f5",
   "metadata": {},
   "source": [
    "We can visualize the solution as follows:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "5098b9fd-be3b-42a8-85f6-47e3466b7eaf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def highlight_cell(x, y, **kwargs):\n",
    "    rect = plt.Rectangle((x - 0.5, y - 0.5), 1, 1, fill=False, **kwargs)\n",
    "    plt.gca().add_patch(rect)\n",
    "    return rect\n",
    "\n",
    "plt.imshow(costs, cmap=\"gray\")\n",
    "\n",
    "for i, j in zip(sol_i, sol_j):\n",
    "    highlight_cell(j, i, color=\"red\", linewidth=3)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a8089186-4d83-4b6b-80e9-f608fab263b8",
   "metadata": {},
   "source": [
    "We can also visualize the solution by drawing it on top of the previous bipartite graph. Below, nodes and edges that are included in the solution are shown in red."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "62df5a9b-0ec5-467f-938b-ec68a4400438",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nx.draw(\n",
    "    G,\n",
    "    layout,\n",
    "    node_color=[\"red\" if i in sol_i else \"grey\" for i in range(n)] + [\"red\" if j in sol_j else \"grey\" for j in range(m)],\n",
    "    edge_color=[\"red\" if (i, j) in zip(sol_i, sol_j) else \"grey\" for i in range(n) for j in range(m)],\n",
    ")\n",
    "nx.draw_networkx_edge_labels(\n",
    "    G,\n",
    "    layout,\n",
    "    edge_labels={(u, v): f\"{info[\"cost\"]:g}\" for u, v, info in edges},\n",
    "    rotate=False,\n",
    "    font_size=8,\n",
    "    bbox=dict(\n",
    "        pad=0.0,\n",
    "        facecolor=\"white\",\n",
    "        edgecolor=\"none\",\n",
    "    ),\n",
    ");"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eca8e6f8-d5a6-4e63-bfe9-7acfeeaf1234",
   "metadata": {},
   "source": [
    "# Optimal transport\n",
    "\n",
    "A linear assignment solver can be used to solve an [optimal transport](https://en.wikipedia.org/wiki/Optimal_transport) problem: Given a [multiset](https://en.wikipedia.org/wiki/Multiset) of points $X \\in \\mathbb{R}^{n \\times d}$ and another multiset of points $Y \\in \\mathbb{R}^{n \\times d}$, find a [permutation](https://en.wikipedia.org/wiki/Permutation) $\\pi \\in \\text{Sym}(n)$ between them that minimizes the total transportation cost:\n",
    "\n",
    "$$ C(\\pi) = \\sum_{i \\in [n]} d(X_i, Y_{\\pi(i)}) $$\n",
    "\n",
    "where $d$ is a [metric](https://en.wikipedia.org/wiki/Metric_space), such as the [Euclidean distance](https://en.wikipedia.org/wiki/Euclidean_distance) on $\\mathbb{R}^d$.\n",
    "\n",
    "Below is an illustrated example where $X$ is a set of _facility locations_ and $Y$ is a set of _client locations_ that must be matched to each other."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "204de132-c37f-4806-ba0f-d8e5c8c7a58b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ss9PmOOeccwCGdHyBYLgQYlGwW2Kz2XC5XKxatWqb41atWkVxcTHZ2dnbHDeYmMD+6C9Dur/tqVaZM888k8cff5wrrriCJUuW8M477/DWW28BCcvScNOXxe3pp59m4cKFTJgwgX/84x+89dZbvPvuuxx++OF9rmEg53X99dezYcMG7r77boxGI7/85S/Zc889MxJ8RoKxzkY988wz2bJlC4888ghFRUXcd999TJs2LU0c9cdIvBbbIznveeedx7vvvtvn30EHHTTg+ZI8+eSThEIhTjjhhLTtJ510EgAff/yxss1ms/HKK69QU1PD+++/T3V1NU899RRNTU3k5eVht9v7PU5RURGQmUgDkJ+fv13r9lDmjEajSsJLf2Pz8/MBhnR8gWC4EAkugt2WE044gccff5yPPvoozTWZ5MMPP6S6uprLL78847mNGzemWZ42bdqEJElpSRfDISAHQkdHB++99x533nknt99+e9oah8pQ1v7CCy9QVVXFkiVL0vb/1a9+NeR1QMJqe+ONN3LjjTeyceNGZs+ezQMPPMDTTz+tjNm0aROyLKcdd8OGDQDKa1JeXs769esz5k9m5JaXl293LYO5Lsn5+nod+lpHX7hcLq688kquvPJKWltb2Wuvvfjd737HD37wg22uZ7hfi2TpqNWrV/c7Ji8vD6vVSjweV5JOhoOWlhZkWc7IDI5GowCKZS6VsrIyxVra2dnJihUrOO2007Z5nBkzZqDT6WhoaMh4rrGxMSPsYiAUFRVRWFjY75xGo1HxWuy99948/vjjGWOTYQhDOb5AMFwIy6Jgt+WnP/0pJpOJyy+/PKPEjMfj4YorrsBsNvPTn/40Y99kaZkkjzzyCIDyIw5gsVjo7Owc/oX3ImkV6m0F2pHOHhaLBWBQ6+9rHZ999hn/+9//hrSGQCCQVo4IEsLRarUqma9JGhsb00rSeL1e/vnPfzJ79mylxMlxxx3H559/nrae7u5uHnvsMSoqKgYURziY6+JyuZg9ezaLFy9Oc/2+++67GfGRvYnH4xnu4vz8fIqKitLO3WKx9OlWHu7XIi8vj/nz5/PEE09kdE1JHkOj0XDaaafx4osv9ikq29ra0h4PtHTO5MmTkWWZ5557Lm37v//9bwDmzJmzzf1vvvlmYrEYN9xwQ9r2devWpZ2L1WrluOOO45NPPklb13fffccnn3yiZNUPlrPOOou6ujreffddZVt7ezuvvPIKhx9+uJKdffLJJ2MwGFi0aFGa9ffvf/87wJCPLxAMB8KyKNhtmTRpEosXL+bcc89lxowZGR1c2tvb+fe//91nyZutW7dy0kknceyxx/K///2Pp59+mnPOOYdZs2YpY/bee2+WLl3KH/7wB4qKijLiloaL7OxsJZ4vGo1SXFzMO++8w9atW4c859577w3AtddeyzHHHINGo+GHP/zhNvc54YQTlMLDxx9/PFu3buWvf/0rU6dOVYL3B8OGDRs44ogjOPPMM5k6dSparZaXXnqJlpaWjLVMnjyZiy++mC+++IKCggKeeOIJWlpaWLRokTLmF7/4Bf/+97/5wQ9+wLXXXovT6WTx4sVs3bqVF198sd+SKqnMnj0bjUbDPffcQ1dXFwaDgcMPP1xxFfbm7rvv5vjjj2fevHlcdNFFeDweHnnkEaZNm7bNa+Lz+SgpKeH0009n1qxZZGVlsXTpUr744gseeOABZdzee+/N//3f//GTn/yEfffdV4mFG+7XAuDhhx9m3rx57LXXXlx22WXKZ+X1119n5cqVAPz+979n2bJl7Lffflx66aVMnToVj8fDV199xdKlS/F4PMp8Ay2ds3DhQu6//34uv/xyvv76a6ZNm8ZXX33F3//+d6ZNm5aW2PT73/+e1atXs99++6HVann55Zd55513+O1vf5tROHvPPffkkEMOSauTedddd/Hee+9x+OGHc+211yrn7XQ6ueWWW9L2/9Of/kRnZ6di+Xv11VeVloDXXHONElt8880389xzz3Haaafxk5/8BJvNxl//+lei0Sh33XWXMl9hYSG33nort99+O8ceeyynnHIK33zzDY8//jhnn332Ngt/CwQjzhhkYAsE44pVq1bJZ599tuxyuWSdTicXFhbKZ599tvztt99mjE2Wzlm7dq18+umny1arVXY4HPLVV18tB4PBtLHr1q2T58+fL5tMJhlQyuj0Vzrn+OOPzzgekFE+JVnuJLWkTH19vbxgwQLZbrfLNptNPuOMM+TGxsaMciwDLZ0Ti8Xka665Rs7Ly5NVKpVS4qSvYyeRJEm+66675PLyctlgMMhz5syRX3vtNfnCCy9MK++yrTlS19ve3i5fddVV8h577CFbLBbZZrPJ++23n/zcc8+l7ZO8dm+//bY8c+ZM2WAwyHvssYf8/PPPZ8y/efNm+fTTT5ftdrtsNBrluXPnyq+99lramGTpnL72l2VZfvzxx+WqqipZo9EMqIzOiy++KO+5556ywWCQp06dKi9ZsiTjmvQ+93A4LP/0pz+VZ82aJVutVtliscizZs2S//KXv6Tt4/f75XPOOUe22+1p5XiG+7VIsnr1auV9ZjQa5SlTpsi//OUv08a0tLTIV111lVxaWqp8no444gj5scceSxs3mNI59fX18kUXXSRXVlbKer1edrlc8qWXXiq3tbWljXvttdfkuXPnylarVTabzfL++++f8X5JPb9DDjkkY/uKFSvkI488UrZYLLLVapVPPvlkecOGDRnjkiWb+vrr/fnavHmzvGDBAjk7O1s2mUzy4YcfLn/++ecZc0qSJD/yyCPy5MmTZZ1OJ5eWlsq33XabHIlEBnSdBIKRQiXLg4hgFgh2c+644w7uvPNO2trayM3NHevlCEjEJE6fPp3XXnttrJciEAgEuyQiZlEgEAgEAoFA0C9CLAoEAoFAIBAI+kWIRYFAIBAIBAJBv4iYRYFAIBAIBAJBvwjLokAgEAgEAoGgX4RYFAgEAoFAIBD0y7guyi1JEo2NjVit1lFrnSYQCAQCgUCwOyDLMj6fj6Kiom02JhjXYrGxsZHS0tKxXoZAIBAIBALBLktdXR0lJSX9Pj+uxWKywXpdXR3Z2dljvBqBQCAQCASCXQev10tpaamit/pjXIvFpOs5OztbiEWBQCAQCASCEWB7oX4iwUUgEAgEAoFA0C9CLAoEAoFAIBAI+kWIRYFAIBAIBAJBv4zrmEWBQCAQCARDR5ZlYrEY8Xh8rJciGAM0Gg1arXaHyw8KsSgQCAQCwS5IJBKhqamJQCAw1ksRjCFmsxmXy4Verx/yHEIsCgQCgUCwiyFJElu3bkWj0VBUVIRerxfNLXYzZFkmEonQ1tbG1q1bmTRp0jYLb28LIRYFAoFAINjFiEQiSJJEaWkpZrN5rJcjGCNMJhM6nY6amhoikQhGo3FI84gEF4FAIBAIdlGGakkS7DoMx3tAvIsEAoFAIBAIBP0ixKJAIBAIBAKBoF+EWBQIBAKBQLDLU1FRwUMPPTTWy9gpEQkuAoFAIBAIdnm++OILLBbLWC9j2Fi4cCGdnZ28/PLLI34sIRYFAoFAIBDs8uTl5Y31EnZahBtaIBDsHGxeBs+eC/86E757daxXIxAIRoi33nqLefPmYbfbycnJ4YQTTmDz5s1AoiTQ1Vdfjcvlwmg0Ul5ezt133w0k6grecccdlJWVYTAYKCoq4tprr1Xm7e2GXrduHfPmzcNoNDJ16lSWLl2KSqVSLHXV1dWoVCqWLFnCYYcdhtlsZtasWfzvf/9T5njyySex2+289tprTJkyBbPZzOmnn04gEGDx4sVUVFTgcDi49tpr07rohMNhbrrpJoqLi7FYLOy3334sX748Y963336bPffck6ysLI499liampoAuOOOO1i8eDGvvPIKKpUKlUqVtv9wIyyLAoFg/LP1Q3j6VJClxOONb8Ppi2D6qWO7LoFgJyQajRKLxUblWFqtFp1ON6h9uru7+clPfsLMmTPx+/3cfvvtLFiwgJUrV/Lwww/zn//8h+eee46ysjLq6uqoq6sD4MUXX+TBBx/k2WefZdq0aTQ3N/PNN9/0eYx4PM4pp5xCWVkZn332GT6fjxtvvLHPsbfeeiv3338/kyZN4tZbb+Xss89m06ZNaLUJCRUIBHj44Yd59tln8fl8nHrqqSxYsAC73c4bb7zBli1bOO200zjooIM466yzALj66qtZu3Ytzz77LEVFRbz00ksce+yxfPvtt0yaNEmZ9/777+epp55CrVZz3nnncdNNN/Gvf/2Lm266ie+++w6v18uiRYsAcDqdg7rOg0GIRYFAMP758h89QjHJF/8QYlEgGAIej4e2trZROVZeXh4FBQWD2ue0005Le/zEE0+Ql5fH2rVrqa2tZdKkScybNw+VSkV5ebkyrra2lsLCQo488kh0Oh1lZWXMnTu3z2O8++67bN68meXLl1NYWAjA7373O4466qiMsTfddBPHH388AHfeeSfTpk1j06ZN7LHHHkBCfD/66KNMmDABgNNPP52nnnqKlpYWsrKymDp1KocddhjLli3jrLPOora2lkWLFlFbW0tRUZFyjLfeeotFixZx1113KfP+9a9/Vea9+uqr+fWvfw1AVlYWJpOJcDisrH8kEWJRIBCMe2KxWOaXVW/xKBAIBoTT6SQ7O3tUjpW0vg2GjRs3cvvtt/PZZ5/R3t6OJCU+67W1tSxcuJCjjjqKKVOmcOyxx3LCCSdw9NFHA3DGGWfw0EMPUVVVxbHHHstxxx3HiSee2Oca1q9fT2lpaZrQ6k9Yzpw5U/m/y+UCoLW1VRGLZrNZEXQABQUFVFRUkJWVlbattbUVgG+//ZZ4PM7kyZPTjhMOh8nJyVEe957X5XIpc4w2QiwKBIJxSywWo7m5mWj+EVSsfw0Vcs+T+/xo7BYmEOzE6HS6QbuGR5MTTzyR8vJyHn/8cYqKipAkienTpxOJRNhrr73YunUrb775JkuXLuXMM8/kyCOP5IUXXqC0tJT169ezdOlS3n33Xa688kruu+8+3n///R0639R9k/21kwK29/PJMX1tS+7j9/vRaDSsWLECjUaTNi5VYPY1hyzLjAVCLAoEgnGHLMt0dHTQ0tICQMGck6G0CD5/HKQo7HUBTD9tO7MIBIKdDbfbzfr163n88cc5+OCDAfjoo4/SxmRnZ3PWWWdx1llncfrpp3Psscfi8XhwOp2YTCZOPPFETjzxRK666ir22GMPvv32W/baa6+0OaZMmUJdXR0tLS2Km/yLL74YlXOcM2cO8Xic1tZW5RyHgl6vT0uaGUmEWBQIBOOKYDBIY2MjwWAQu91OYWFhwo3kPAYmHzPWyxMIBCOIw+EgJyeHxx57DJfLRW1tLb/4xS+U5//whz/gcrmYM2cOarWa559/nsLCQux2O08++STxeJz99tsPs9nM008/jclkSotrTHLUUUcxYcIELrzwQu699158Ph+33XYb0GM9HCkmT57MueeeywUXXMADDzzAnDlzaGtr47333mPmzJlKfOT2qKio4O2332b9+vXk5ORgs9lGzGIsSucIBIJxQTwep6mpic2bNyNJEpWVlZSUlAwp5kkgEOycqNVqnn32WVasWMH06dO54YYbuO+++5TnrVYr9957L/vssw/77rsv1dXVvPHGG6jVaux2O48//jgHHXQQM2fOZOnSpbz66qtpcYBJNBoNL7/8Mn6/n3333ZdLLrmEW2+9FQCj0Tji57lo0SIuuOACbrzxRqZMmcIpp5zCF198QVlZ2YDnuPTSS5kyZQr77LMPeXl5fPzxxyO2XpU8Vg7wAeD1erHZbHR1dY1aMK5AIBhdZFnG6/XS1NREPB4nPz+f3NzcEb+7Fwh2ZUKhEFu3bqWysnJUxM+uwMcff8y8efPYtGlTWmLJzs623gsD1Vnill0gEIwZ4XCYpqYm/H4/VqsVl8uFXq8f62UJBILdgJdeeomsrCwmTZrEpk2buO666zjooIN2KaE4XAixKBAIRh1Jkmhvb6etrQ2tVktZWZnwHggEglHF5/Px85//nNraWnJzcznyyCN54IEHxnpZ4xIhFgUCwaji9/tpbGwkEomQm5tLfn4+arUInxYIBKPLBRdcwAUXXDDWy9gpEGJRIBCMCtFolObmZrq6ujCbzZSVlY2/WKqGFbDiyUTB770uhNK+i/QKBALB7oQQiwKBYESRZRmPx0NLSwsqlYri4mLsdvv4S2Cp+R8sPgGk73vmrvw3nPciTDhsbNclEAgEY4wQiwKBYMQIBoM0NDQQCoVwOBwUFBSM31I4n/21RygCyPHENiEWBQLBbs44/dYWCAQ7M/F4nJaWFjweD0ajkaqqKsxm81gvq18kSSLW3UlGHnakeyyWIxAIBOMKIRYFAsGwIcsyXV1dNDc3I0kShYWF5OTkjD+X8/dIkkRnZydtbW2YCg+jrGZ5+oBZZ4/JugQCgWA8IcSiQCAYFsLhMI2NjXR3d5OdnY3L5Rqx1lM7SrL3dFtbG9FoFJvNRt5hV0CBE774eyLBZe+FMOfcsV6qQCAQjDmiXoVAINghJEmipaWFTZs2EY1GKS8vp6ysbFwKxaRI3LBhA42NjZhMJiZOnEhpaWkiM3uvC+DyD+CKj2DfS8Z6uQLBboksy1x22WU4nU5UKhUrV67cofnuuOMOZs+erTxeuHAhp5xyivL40EMP5frrr9+hY+zqCMuiQCAYMj6fj8bGRmKxGLm5ueTl5Y1NzURJgngYdKY+n5ZlWXE3RyIRsrOzKS8vH3+lewQCAW+99RZPPvkky5cvp6qqitzc3B2a76abbuKaa67p9/klS5ak3dxWVFRw/fXXCwGZghCLAoFg0ESjUZqamvB6vVgsFioqKjAYDGOzmG+ehaV3gK8JyufBKX8BRznQE0PZ2tpKJBLBarVSWlqKydS3qBQIBGPP5s2bcblcHHjggcMyX1ZWFllZWf0+73Q6h+U4uzLCDS0QCAaMLMu0t7ezceNGAoEAJSUlYysU2zbAyz9OCEWAmo9gyWWKSNy0aRP19fUYDAYmTJhAeXm5EIp9IcsQ6hrrVQjGKW2+MP9d10JjZ3DEj7Vw4UKuueYaamtrUalUVFRU8NZbbzFv3jzsdjs5OTmccMIJbN68OW2/+vp6zj77bJxOJxaLhX322YfPPvsMyHRD9ybVDX3ooYdSU1PDDTfcgEqlQqVSKXHYL7zwQtp+L7/8MhaLBZ/PN6zXYDwiLIsCgWBABAIBGhsbCYVCOJ1OCgoK0Gg0Y7omeeM7qGQpfWPdp2xZu5KgrCMrK4vi4uJxXbZnzNn8X3jtJ9CxFXKnwMl/Ep1rBAr//ryW219ZTTQuo1GruOnoKfz40Akjdrw//vGPTJgwgccee4wvvvgCjUbDBx98wE9+8hNmzpyJ3+/n9ttvZ8GCBaxcuRK1Wo3f7+eQQw6huLiY//znPxQWFvLVV18hSdL2D9iLJUuWMGvWLC677DIuvfRSACwWCz/84Q9ZtGgRp59+ujI2+dhqtQ7b+Y9XhFgUCATbJBaL0dLSQkdHB0ajkQkTJoy5dS4ej9PZ2Uk4qKWo13MxvQ2NyUpVYZEQidsj5IX/uwAi31tG2tfDs+fCDWtAm1F1UrCb0RWMcuera4jGZQDiksx9b6/jpNlFFNtH5jvAZrNhtVrRaDQUFhYCcNppp6WNeeKJJ8jLy2Pt2rVMnz6dZ555hra2Nr744gvFpTxx4sQhHd/pdKLRaLBarcrxAS655BIOPPBAmpqacLlctLa28sYbb7B06dIhnunOhXBDCwSCPklmDm/cuJGuri5cLteYC8VQKERjYyPr16+nqamJ2ISjiLj2SRsTP+RmKqomCqE4EGo/7RGKSbpboembsVmPYFyxuc1PKJpunZNk+K7RO6rr2LhxI2effTZVVVVkZ2dTUVEBQG1tLQArV65kzpw5Ixp7OHfuXKZNm8bixYsBePrppykvL2f+/PkjdszxhLAsCgSCDJKiLBAIYLPZKCwsHLNSOLIs4/P5cLvddHd3o9VqcTqdGAwG3G43Gw54gLy2/+GgC/3U4zC4Zo7JOndKvk8ESkVWaQjpcxCRnYLJBVayDFr84Z42mDqNipkltlFdx4knnkh5eTmPP/44RUVFSJLE9OnTiUQiAKN2A3vJJZfw5z//mV/84hcsWrSIH/3oR+O24cBwI8SiQLAbE5dk/vr+Zl5b1YTDrOPy+VVMsUm0t7ej1+upqKjYZhbhSBKLxejo6MDj8RCNRjGbzRQXF6PRaGhra6O9vR2z2UxF1USyZs4ekzXu9ORNgTnnw9dPKZs69ziHhrYAznhjWlxqMBLHpB/bGFXB6JJl0HL3qTO4ecm3+MMxjDo1tx0/lfzs0Ss55Xa7Wb9+PY8//jgHH3wwAB999FHamJkzZ/L3v/8dj8czLNZFvV5PPB7P2H7eeefxs5/9jIcffpi1a9dy4YUX7vCxdhaEWBQIdmMefHcDf1q2SXn82RY3Dx7nYv8pJeTm5o5JzcRAIIDH46GrK5Gda7PZcDqdxONxWltbCQaDCZFYUYHFYtlt7uxHjJMegemnQfMqKNkXe9kBxN1uWltb8Xq9bA2ZuOfdLVS7A0wvzuae02YyrWh0LUuCsePEWUUctkc+65t9TMizYDePbiyrw+EgJyeHxx57DJfLRW1tLb/4xS/Sxpx99tncddddnHLKKdx99924XC6+/vprioqKOOCAAwZ9zIqKCj744AN++MMfYjAYlDqPDoeDU089lZ/+9KccffTRlJSUDMs57gyImEWBYDfm+RV1aY/jMqzs0JOfnz+qQjHZo3nz5s1s2bKF7u5u8vPzmTx5Mna7nebmZmpqagAoLy+nsrKSrKwsIRSHA5UKJhwGB10H5QeiUqnIzc1l4sSJRFU6rn9+DdXuAACrG7xc9s8VxCV5jBctGE2yDFr2LneMulAEUKvVPPvss6xYsYLp06dzww03cN9996WN0ev1vPPOO+Tn53PccccxY8YMfv/73w+5WsOvf/1rqqurmTBhAnl5eWnPXXzxxUQiES666KIhn9POiEqW5XH7qfd6vdhsNrq6usjOzh7r5QgEuxzz711GrSeQtu3qwyZy0zFTRuX40WgUj8eDx+MhHo9jsVjIycnBarUSCARoaWkhEAhgMpnIz88XAnGUefPbJn78r68yt193MHu6xHfyeCYUCrF161YqKytFp6Jh5KmnnuKGG26gsbERvX7nqBiwrffCQHWWcEMLBLsxFx1UwR2vrlUeWw1aztq3dESPKcsy3d3deDwevF4varVaKbZrMBjo7u6murqa7u5ujEYjZWVlWK1WIRLHgGJHZuKATqMi3zpGRdgFgjEiEAjQ1NTE73//ey6//PKdRigOF0IsCgS7MQsPqqQg28hrq5qwm3X86KAKSp0jU3ImHo/T1dWF2+0mHA5jMBhwuVzY7XY0Gg2BQICtW7cKkTiOmFli5/gZLl7/tknZdunBVeRkCbEo2L249957+d3vfsf8+fO5+eabx3o5o45wQwsEghElHA7j8Xjo6OhAkiSys7OVllwqlYpAIEBrayt+vx+DwUB+fj7Z2dlCJI4TJElm2fpW1jX72KfcwX5VOWO9JMEAEG5oQRLhhhYIBOMSWZbx+/243W78fj8ajQan04nT6VTcN8FgkJaWFkUklpaWCpHYH7EwrH0FOqphwuFQss92dxku1GoVR+xZwBF7FozaMQUCwfhiRMXi3XffzZIlS1i3bh0mk4kDDzyQe+65hylTRid4XiAQjC7xeJyOjg7cbjfRaBSj0UhxcTE2m03Jrg4Gg7S2tuLz+dDr9ZSUlGCz2YRI7I94DBafBHWfJh4v+x0cew/sf8XYrksgEOw2jKhYfP/997nqqqvYd999icVi3HLLLRx99NGsXbsWi8UykocWCASjSDAYxOPx0NnZCUB2djY5OTmYTCZFBAqR2A/d7Ym2e7mTIW9y5vMb3uoRikmW3wX7XCT6NwsEglFhRMXiW2+9lfb4ySefJD8/nxUrVuw2/RQFgl0VWZbxer243W4CgQBarZa8vDycTidabc9XSygUUgo86/V6iouLsdvtQiQCrF4CL10B8XDi8X4/hh/8Pm2I3FVPxpUKdUHED9qR64UrEAgESUY1ZjHZkaG/djzhcJhwOKw89npHt1m5QCDYPtFoVGnDF4vFMJvNfcYbpopEnU4nRGJvYmF446YeoQjw2aMw6ywomgNAJBKh1TyVYpUGlZzSfqx0PzALoSgQCEaHUROLkiRx/fXXc9BBBzF9+vQ+x9x9993ceeedo7UkgWDnZMM7sPEdsJfBXheAyT7ih5RlmWAwiNvtVm7ikrURe2fXhcNhWltb6erqQqfTUVRUhMPhECKRRExnMBgkFAoRad1IUcCdOaj5W2TXbDo6Omhubkatzyd43COYP7obuuqgcj6c9KfRX7xAINhtGTWxeNVVV7F69eqMBuCp3HzzzfzkJz9RHnu9XkpLR7ZAsECwU/HB/fDf3/Q8/vppuGw56EemNqIkSUptxFAohF6vp6CgAIfDkdFKqy+RaLfbx6S/9HggFosRCoUIBoM9AjESAUClUmHU5xC3FKLpbk7bL1K4Nw3fFyV3OBwUFhai0ewB+54L8ShodGNxOgLBmFNdXU1lZSVff/01s2fPZvny5Rx22GF0dHRgt9vHenm7NKMiFq+++mpee+01Pvjgg2023jYYDBgMotirQNAXciwCHz+UHr/Wvh6++w/M+uGwHisSiSi1EePxOFlZWZSXl/fZbi8cDtPW1kZnZydarRaXy4XD4ditRGIsFksThcFgkGg0CiR62xqNRqxWK0ajEZPJhMFgSFzH0x6DFy6CQDuyxkBgv+up7gCtNkJFRQVZWVnpBxJCUSBQOPDAA2lqasJmsw3bnL0FqSDBiIpFWZa55ppreOmll1i+fDmVlZUjeTiBYJdBkiRCoVDaX9jfwR5hf+bggGdYjplsw+d2u/H5fKjVahwOB06ns8+buEgkQmtr624nEqPRaIbFMFUYmkwmsrOzMZlMmEwm9Hp9/y74qkPgJ2uJ1K+kMaDDL+lxOhwUFBRkWG4FAkE6er2ewsLCsV7GbsGIisWrrrqKZ555hldeeQWr1Upzc8LdYrPZMJkye44KBLsbsiwr4iP1L+muhITF3Wg0YnWVEa86Au2WpT0TaPSwx/E7tIZ4PE5nZycej0dpw7ctF3IkEqGtrY2Ojg60Wi2FhYU4nc5dTiTKstynxTAWiwGg0WgwGo3K95nRaNy2MOznGO5OHy3dWeh0OiqLi3vKisVj8OH98O0LibjUg66HPU8Y/hMVCLaHZyvUfwmumZA38nWSJUni/vvv57HHHqOuro6CggIuv/xyzj333LRxfbmhP/roI26++Wa+/PJLcnNzWbBgAXfffbfyuaqoqOCyyy5j06ZNPP/88zgcDm677TYuu+wyAMWoNWdOIsnskEMOYfny5SN+zuOdERWLjz76KACHHnpo2vZFixaxcOHCkTy0QDDukCSJcDisCMJgMEg4HCYeT2S5JsVH0l1pNBoxGAzpIuz0x+GtX3yf4FIOR/wSHOVDWk84HMbtdtPZ2am04SsqKsJsNvcpeJIisbOzE7VavUuJxFTRnhSHwWAw7bUxmUzY7XbFYqjT6XYoaScUCtHQ0EAwGCQnJ4eCgoL0a7n87oRYTPLc+XDRO1C675CPKRAMmv/9Gd65DWQp8fjgmxLfOyPIzTffzOOPP86DDz7IvHnzaGpqYt26ddvdb/PmzRx77LH89re/5YknnqCtrY2rr76aq6++mkWLFinjHnjgAX7zm99wyy238MILL/DjH/+YQw45hClTpvD5558zd+5cli5dyrRp05SOU7s7I+6GFgh2N5IWqQw3ckpZKL1ej9FoJCsrSxGGAxIfZiec+tgOrc3n8+F2u+nu7kaj0ZCTk4PT6USn6zseLhqNKpZEtVpNfn4+OTk5O61ITArDVFEYCoUUYajVajEajTidTsViuKPCsPfx29raaGtrQ6/XU1VVhdncR4LSN8/22lGCb5/bvcRisAOqP05k/rtmjvVqdj8CHlh6Z49QBPjwAZhzHjhHJqzM5/Pxxz/+kT/96U9ceOGFAEyYMIF58+ZRXV29zX3vvvtuzj33XK6//noAJk2axMMPP8whhxzCo48+qlRuOO6447jyyisB+PnPf86DDz7IsmXLmDJlCnl5eQDk5OQIF3cKoje0QLAD9LYWJv+SwiOZ3GCxWJQyM0ajcdSFViwWU2ojRqNRTCYTJSUlZGdn97uWaDRKe3s7Ho9HEYlOp3OniqWTZZlIJJLmRg4Gg0hS4sdPq9ViMpmU1yZpMRwpgsEgDQ0NhEIhcnNzyc/P7/P6y7KMpDWScaV1I5P1Pi7ZuBSeuwCi3YnHM85M3CiJEkyjh3tzeh1QAGRoWzdiYvG7774jHA5zxBFHDHrfb775hlWrVvGvf/1L2SbLMpIksXXrVvbcc08AZs7sufFQqVQUFhbS2tq644vfhRFiUSAYIKnWwqT4SLUW6nS6NOEx3BapoZCsjZgsiG+z2ZQ2fP2RKhJVKhV5eXnk5OSMe5Eoy7Ii3FMthklhmHx9cnNzFVdyaqeZkUSSJDwbPkX65nlsRivFB12CKbdvq0UsFqOxsRF15RmUeO7uecKQDXsv3P7B1r0O//0tdDXA5GPguHvB5BieExktZBneuLFHKELCqjrrLJh45Nita3ejYBoYbYmOQUk0BigZOev2juQz+P1+Lr/8cq699tqM58rKypT/974hVKlUyveEoG+EWBTsNmxq9fO/LW4m5Fk4cEJuv+NSRUfqXzKxQa1WYzAYMJvNOJ1ORRiOFzElSZLShi8YDKLT6cjPz8fhcGxTHMViMdra2nYKkZh8jVIthn0Jw7y8PMViOFrCsDeBQADPipcoWnYdaimRNc2GZ+DS/ybcqyl4vV4aGxuRZZmi+T+GPfaB1S+A0Q5zL92+NadtQ8IaJyXeq3z7HMSCcNbTw39iI0nYBx3VmdubvxVicTTRm2HBY/DKlRBwg8EGx90Hlv6/P3eUSZMmYTKZeO+997jkkksGte9ee+3F2rVrmThx4pCPn4xRTHqHBAmEWBTsFjz1v2pu/88akmG0x8908edz9uo3tjAZb6vT6TAajTgcDkUUDjbjdbSIRqNKbcRYLIbFYqGsrAyr1brN9cZiMdrb23G73ahUKnJzc8nNzR03IlGW5TSLblIYJl8jvV6PyWTCarUqFsPxsHZJkmhtbaW9vZ0J3/6jRygCdLfB54/B0b8FEj9MTU1NdHZ2YrVaKSoqSlg/bEfCpEGIo3Wv9ghFZdsbEIuAducI1I9Go7S0e8m1TcDYtTn9ybIDxmZRuzNTjoWffAeeLYmkuhFqAJDEaDTy85//nJ/97Gfo9XoOOugg2traWLNmzXZd0z//+c/Zf//9ufrqq7nkkkuwWCysXbuWd999lz/9aWBdj/Lz8zGZTLz11luUlJQoFQ92d4RYFOzyBCNx7n1rPan5Vq+vauKw4q/ZIyfhjlCpVIoFKlUYjgfRkcqq+k7ufHUtaxu97F3u4I6TpuKyqJU2fGq1Grvdrlg8t0VSJHo8iTqNubm55OTkjJkFDnpiQFNFYaowTJYRSi1XM95eI0hYE+vr64lGoxQUFGCMdWYO8iVKifn9fhoaGojH4zvcPzukziLjVTfZQT3+v+rj8ThtbW243W7UajVZxzyA4a0rUXkbQa2Dg66Fsv3Hepm7J1oD5O85aof75S9/iVar5fbbb6exsRGXy8UVV1yx3f1mzpzJ+++/z6233srBBx+MLMtMmDCBs846a8DH1mq1PPzww/z617/m9ttv5+CDDxalcwCVPI5Tlr1eLzabja6uLrKzs8d6OYKdlDpPgIPvXZax/bajyjl97xKlRM14tBamEozEOeie/+Lp7qnBWJyt49ETXRgNBnJycrDb7RniaVV9J52BKPtVOTFoNcTjccWSKMsyOTk55ObmjrpITBYeT3Ulp1p1DQaDYikcr+K9N5Ik0dLSgtvtxmQyUVxcTCwWI/z6zeR898/0sWcsptkxF4/Hg8Viobi4eMhlOqLRKE1NTfjdTUxcdil6b03Pk8fcDQdcuSOnNaJIkoTH46GtrQ1JktIt2/EYtKyG7GLIyhvrpe5UhEIhtm7dSmVl5XZvHAW7Ntt6LwxUZ43/202BYAcpcZiozLWwtb0nWF6jVnHMnCrs9p0nu/TTLe40oQjQ4I0SMuYyY2JhZhu+WJxL/7mCDza0AZCXZeDBUybgVAdHXSSmCsNUi2GSpBh0OByKONzZSvP4/X4aGxuJRqMUFhbicDhobW3F7XZj2ftq7CYNmm+fA72ZyD5XUK2bSrSjA5fLhdPpHNLNiizLeDweWlpaUKlUFFVOQTflfVj5L+iqT7gQqw4d/pMdBmRZpquri5aWFqLRKA6Hg/z8/PTkA40WimaP2RoFAkECIRYFuzwqlYpHzp7Dtc9+zZa2bpwWPbcetyelzp1HKALkZGVanVQqKM7r2235wop6RSgCtPnD3L90C4+eNZW8vLwRE4nxeLxPi2FivSrFYpiaHLSzCcNU4vE4LS0teDwezGYz5eXlSJLEli1biEQiFBYWkpOTg2riQ0gn/EGJYzRpNJSXl/fZSnEgBINBGhsbCQaDOL5vEai8pgdePYxnOPz4/X6am5sJhUJYrVYqKiqGfB12a+IxePeX8NU/E6EG+10Oh94sygsJhh0hFgW7BdOLbfz3xkNp7grhtOjRa3c+cTKzxM7he+Tz33U99cDO2LuEYnvfpSbWNHoztlV3xXG5XMO2png8nlHDMNmqMBkHmqwxaTKZMjvS7OT4fD4aGxuJx+NKb2y3201raysGg4EJEyYobp9kjcVwOEx+fj55eXlDsiamJs4YDAYqKyt7WgSOJpIE7/++R6jMvRQOum6buwSDQZqbm+nu7sZsNo/d2ncVPn4IPv1Lz+P37wFbKex1/pgtSbBrIsSiYLei0LZzx+789by9+c83jaxp7GLvcgfHTe9f+O1V5uCZz2rTt5UPvd5eMnM81ZXcWxhmZWUpcYY7QxzoUEnNXk7GGwJUV1cTCATSCm731bFlqLXkvF4vTU1NxGIxCgoKxraTzmePJsRJkndvB0s+zD47Y2gkEqGlpYWuri70ev2AsvQFA2Dd631se02IRcGwI8SiQLATodeqOX3vEk7fu2S7Y0+ZXcSHG9t4ZWUjAFW5Fm4/YeqAjhOLxdJEYTAYJBpNlH5JdqVJ9rDe1YVhb5K1ECVJoqioCLvdTldXF01NTWg0mjRrWTgcpr6+nmAwuM2OLdsjmcDi9XrJysoaH27bNS/1vS1FLKbW7tRoNBQVFeFwOHab98pIIssyUYOTjOAUa2HGOMHuzXC8B4RYFAh2UbQaNX/84RxuOnoKnYEo04qyUaszf6Sj0WiGxTBVGJpMJrKzsxWL4XitMznSxGIxmpqa6OrqIisri6KiItRqNXV1dfh8Pux2Oy6XC41GoySeNDc3o9Pp+u//vB1SE1jUajUlJSXYbLYxv/6SJBHVZJEhV805yvNut5u2tu+Tq/LyyM3N3aVCEMaSSCRCfX09csWZVNZ9jDoWTDxhtMEBiXjVZKJQIBDYoa4ogp2fQCAAZHauGQxCLAoEuzilTjOlzu8tEdFohsUw2ZlGo9Fk1DDcXYVhb7q6upTOKslaiH6/n/r6eiDRSixZdiISidDQ0EB3dzdOp5PCwsIhiaTUBBan00lBQcG4KB3k8/loampCV3kGFXUfoUoWG9dZkA+4ks6ODlpaWojFYjidTvLz88e0dueuROrNg0ajoXjv41HP3A9WPZ/IHJ/5Q8hOhKZoNBrsdrvS89hsNovP8m6GLMsEAgFaW1v7LKs2GESdRYFgFyQpDFMthsFgUGlhpdFoFEGYtBiOdR/r8UiyT7PX61U6q6jVapqbm+no6CArK4vi4mJ0Oh2yLNPZ2am4o4uLi8nKyhr0MePxuFJyx2AwUFxcPCSr5HATiURobm7G6/VisVgoKirC0LUVvnkGWaXFP+lkmiNmwuEwNpuN/Pz8sXeV70L0vgkZyM2DLMs0NzfT2dk5OosUjEvsdjuFhZnl1WDgOkuIRYFgJ6e3xTBpNUwKQ61WmyYKjUajEIbbIVkDsKmpCYCioiKys7MJBoNKZ5Zk9rNKpSIajdLY2Jjhjh4sqQks+fn55ObmjvnrJMsy7e3ttLW1oVarKSwsTHOFBwIBmpubCQQCWCwWCgoKxoW4HRbGQZtEWZbp6Oigubl5yDch8XhcCS0R7F7odLptfheJotwCwS6ILMtEIpGMcjWSJAEJYWgymcjJyVEE4o7EqeyOpAo/m82mCL/W1lba2towmUxp9RGTLmpId0cPhkgkQlNTEz6fj6ysLCorK4fczWU46e7uprGxkXA4TE5ODvn5+coPTzgcpqWlBa/Xi8FgoLy8nKysrDEXt8PC+jfhrZuhYyuU7g8n/wlyJ436MlKtiQ6Hg8LCwvQf/pXPwIcPQLATZpwOR94JusyKDxqNZlyEMAh2XoRYFAjGKbIsEw6HM5JPksJQp9NhMpnIzc1VrIYiNmzopLqR1Wq1IvzC4TA1NTUEg8G0+oipCS/Z2dkUFRUN+vrLsqzUZVSr1ZSWlpKdnT3mgisWiynuS5PJxIQJE5QkiVgsRmtrKx6PB51Ot8P9rMcdvmZ47gKIf98tqe7TxOMr/zdqS0i1JqrVasrLy7FarT0DmlfDty/Axw/2bPvsr6DSwLF3jdo6BbsP4pdFIBhhZFnmuS/rWL6+jVKnmYsOqsyo95gUhqkWw76EYV5enmIxFMJw+IhEIjQ2NuL3+5X4Ho1Gg9vt7jOj2efz0dDQgCRJQ85QThbpDoVC4yaBpXf7wFQhGI/HcbvdtLe3A4x9nceRYvN/e4Rikta10FENjooRP3w0GqWhoUF5L2aENLx7O3z8x753XrNEiEXBiCB+bQSCEeauN77j8Q+3Ko9f/aaR//x4Llo5vZZhMnxYr9djMpmwWq2KxXCsRcSuSn8WnGg0Sk1NDX6/Py2jOR6P95ncMhhSE1iMRmOPCP3wDwnrUDwKe10AR9wO6tF73QOBAI2NjYRCobT2gUnrZ1tbG/F4fFR7io8F8SwXGVdda1LKAo0UvS3bGdZEAPdm+Pjh/icZ4TUKdl92zU+7QDBOCMfiPPVpTdq2pq4QTy1fzdETrRgMhoxyNUIYjg79xYMlYxBVKlXaD7bf76ehoYF4PD6k4tKyLKe1B1R6RqtUsPLf8N6dPYM/fghMDph3/fCedB/EYjFaWlro6OhIE6/JJJ+WlhYikQh2u538/PxxEUs5UgSDQWpjLooL9yOr+bOeJw6+EQzW/nfcQQacINW+AegvJ1WVWKdAMAIIsSgQjCCSBNF45pd7lt3JnntOFMJwDEgtmK3VaqmoqCArK4t4PE59fT2dnZ1pMYiSJNHS0oLb7Vb6GQ9WMKUmsFitVlwuV/oca1/J3OnTv0BnbSJxofzAHTzrTJKWrObmZmRZxuVy4XQ6UalUdHd309zcTDAYJCsri9LS0l26sHPSwtzU1JSoL7rwZdj8NrRtgMr5UH7AiB03eXOSGifbH37HNMwaA+p4uGcOrRHVXhfAjDOgdO6IrFMgEGJRIBhBTHoNx89w8Z9vGpVtWQYtp+xdLoTiGBAOh2loaCAQCKTFCXZ3d1NfX088Hk+L0wsEAjQ0NBCJRNItgQNkIAkssiwT0dsyu6H4W+DLf8CXT8Bpf0+IxmEiFArR2NhIIBDAZrNRWFiITqcjFArR0tKCz+fDaDQqQnpXRpIkGhsb6ezsTC+iPm3BiB63r6z7/lz7yf7ira1ecg+4g9zPf4820oWcVYDqlL/AxCNHdK0CgaizKBCMMMFInAeXbmDZulZKnWauO2ISs0rtY72s3YpkrcDW1lYlg9disSBJEq2trbS3t2M2mykpKUGv1yNJEm1tbbS1tWE0GikpKcFozCxJsi1SYwD7S2BJCoZIwyomLLsCddTf92QFM+DHHw319BV6F/x2uVxkZWURjUZpbW2lo6MDnU5HQUHB0NsKShLsJEkv4XCY2tpaIpGIcpMw0vSu4VlcXLzN37dYLEZ9fb0SP9vV1YVBI1Nu16DJqQKNKI0lGDqiKLdAIBCQsKI1NDQQDAbJycmhoKAAtVpNKBSivr6ecDicVgA7uT0UCqWVyhko8XiclpYWPB4PRqORoqKijCLVvZMZioqKyJY6E7GL616D5lXpk9pK4YbVQ74GsiwrBb/j8Tj5+fnk5OQoFiu3241arSY/Px+HwzG0DOeAB169Fta9AZY8OOxm2HvhkNc80nR1ddHQ0IBWq6WsrGzQNwNDIbUj0PasiZCoc1lXV6eECSSz1KuqqnbZBCPB6CKKcgsEgt2apBBqa2tDr9enJW60t7fT0tKibDeZTCmuvlb0en1abcGBHi8pyCRJ6tdt3btMT08yQzYc+nPipfujeeqk9Ml3wAUdDodpbGyku7ub7OxsCgsL0Wq1eDwe2trakCSJ3NxccnNzdyw04rUb4LtXE//3N8Or10H+NCjdd+hzjgCpMag2m42ioqJRCQlJxiYaOjczZf3j6NrXJa7NMXeBvSxtbOp71Gw2U1RURH19PbIsU1lZKYSiYNQR7ziBQLDLkVrDMDc3l/z8fNRqdVoGdKqVMTWWMXX8QEkVgH0msDCAQsvfj6lVl6Hf7w5cW/4PddiXEIqH3Troa5B0pbe3t6PVapUOK8kM52g0isPhID8/f1i6/Mjr3yDD/rr+jXElFqPRKLW1tYRCobSEnpEk1ZqYbTZQ+vFPUPlbEk9+9yq0b0oU/P5+HbFYjIaGBnw+H7m5ueTl5Smu8qqqql06G10wfhFiUSAQjA6SBJ/+OZH5a8mDeTcMe/ZmaqyhwWBQrINJt29jYyMajUZJ3EgmoCQzoysrK7FYLAM+XmospEaj6Tebdbtt276fq6mpie7ubvIOvhT1D24Y8nVI7TGdFByBQIDNmzcTCoWwWq2Ul5cPi+s1EAjg8XjIN+ai725MfzK7aIfnHy78fj91dXWo1WoqKytHpX91aivI0tJSsls+6xGKSdq+g5bVUDiDQCBAXV0dkiQp4r6uro5AIEBFRcWouMoFgr4QYlEgEIwOy34HH97f83jzf+GKj4at524yczk1BlGtVmfEiSXdjqkCbigdVFKP17tvcpL+yvT0hcfjwePxUFRUNOQM5N49pisqKpAkidraWvx+PyaTadCCuC8kSaKrqwuPx0MwGExkUh/4U3RLb0QlJ7oOkTsZZp61Q8cZDlLDC7KysigpKRlxN25qK0ir1UpxcTFarZZwuykz6x2QDVY839+0GI1GSktL0el0yvu2rKxsh18zgWBHEGJRIBCMCvKKJ9PdlLEQfPMsHPHLHZo3NaPZaDQyceJExQKTbMsnyzKlpaXYbLa0mnr9dsrYBr0TWPqLbeyvTE9f+Hw+mpqayMnJwel0DukatLe309bWhkajobS0FKPRSGtrK11dXej1esrKyrBarTvkdo1EIng8Hjo6OojH42RlZfXMO2UKTNgX1r0OWQUJ9/kIFrIeCKmZxENJVhoKXq+XxsZGZFlWWkFKkkRTUxPuoIOq/L0wt36ljJemnUq9T43X25QWGpEslL69bGmBYDQQYlEgEIwYsiwTDAbp7OwkT4KMyDj1jn0FdXd309DQQDQapaCgQMloliSJ5uZmPB4PFouFkpISdDpdWjzYYJMbeiew9BfzlnRtt7S0oNPptmvJC4VC1NXVYbVaKSwsHPQ18Pv9ifI7kQi5ubk4HA48Hg/19fVoNJohdZvpfT7d3d243W58Ph9qtRqHw4HT6cRg6GUnK5yR+BsH9HbpDuaGYCj0tiYmi7qnZqEXFBRgvPhV+PppaP6WSOEcqu0HEvP700IYku0VCwoKcDgcI7pugWAgCLEoEAiGnXA4TGdnJ11dXUQiEbRaLdaZ56P7/MGeQXorzD57SPOnZrSaTKa00ifBYJD6+noikUiaoOsdP2az2QZ8vNQEluzsbFwuV59JIf2V6emPWCxGTU0Ner2ekpKSQQm6aDRKc3MzXV1dSo3I7u5uNm/eDEBeXp7iih8K8Xiczs5O3G43kUgEg8FAUVERdrt9yHOOBqmu/6RLd6STQpLWREmSlHqNkUhE6S/eO+lJ3u9yxbpt0OqZUFqqCO9kDcZkD26BYDwgxKJAIBgWYrEYXV1ddHZ2EgwGUavVSts8i8WCao87wDWxJ8HlgKvAUTHo4yR7NMdisbTyNKmxaUn3sNFoJB6P09jYmBE/NhBSE1iS9fj6cgn2LvqdLNOzLZKxhLIsU1ZWNigLZ7IrjEqloqgokURSW1tLLBbD6XSSn58/5Li8UCiEx+Ohs7MTSZKw2WwUFxdjNpt7xGw0BF8/BQ1fQfFesNcFoO0rGm90SX2tByLWh+N4TU1NdHZ2kpWVRXFxMRqNRgmL6Os9k7rGtI4xJN7b9fX1SledkXaZCwQDRRTlFggEQ0aSJHw+H52dnfh8PgCsVit2ux2r1TqsP9SpsYJms5ni4mLFGhMOh6mvrycYDJKXl0deXh5qtVqJWUy6jZNt/AZCd3c3jY2N20xgAdKKeA+07I4sy9TX1+P1egeVmZvaFcbhcGCxWGhrayMcDpOdnU1BQUGma3gAJF3sbrebQCCAVqvF6XTicDj6Lqvz9GmwaWnP48k/gHOeHfRxh5OkOz8ajVJcXDwoy/FQ6Ou95ff7aWpqIhqNKlnoqe+F1DUmrbRJgsEgW7duxWw2U1ZWNq6tt4JdB1GUWyAQjAjJGLbOzk68Xi+SJGEymXC5XNhsthHJNPX5fDQ2NhKPx9Ncy6m1CzUajRIfmLTeJGMWi4uLB+yKjMfjNDc309HRgclk6jeBJTWpJLXo90Boa2ujq6uL0tLSAe0Ti8Vobm6ms7MTk8lEcXExHR0ddHR0KOc3lFIw0WiUjo4OPB4PsVgMs9lMaWnptoV+87fpQhFgw5vQug7y9xj0GoaDZFkknU7HhAkThiSYB0pva2LSsltXV4fX68VisVBeXp6xho6ODhobG5WC76nPh8NhqqurMRgMlJaWCqEoGHcIsSgQCAZEKBSis7OTzs5OYrEYOp2OnJwc7Hb7iP04p/4w9xZ9qckqqbULu7u7qa+vJxaLDarwcmrP3mR7tf72TS36nWrJHAhdXV20traSn5+/XetXUgy3tLQgyzL5+flKXKTBYFBq8Q3GXSnLslIb0ev1AmC328nJyRlQHT8p2EmfZxrqGvAahovURKaku3wkhVaqNTFpGfR4PLS2tqJWq5Xs59TXQ5IkGhsb6ezsxG63U1RUlLbGaDRKdXU1Go2G8vLyUekmIxAMFiEWBQJBv0SjUSUOMRQKodFosNls2O12TCbTiMZUpSYN9M7o9Xq9NDQ00OqPobM62dNVhAqZ5uZm2tvbMZvNVFRUDFjE9m6J118CS2rR722VzemPZPKNzWYjLy9vu2MbGxsJBoNkZ2ejVquV2MlkEsVgrr8kSXR2duLxeAiFQuj1eiXbdiACJSmmm4MOqswu9IGmniedVVCyz4DXMhxEIhHq6uoIhUI7nPG9PVKtzcmblmg0yubNm7cZphAOh5XuK8XFxRmZzfF4nJqaGtHGTzDuEe9MgUCQRjwex+v10tnZSXd3NyqVCqvVSn5+PllZWSPuIkstQZJMGkgKt+SPtsfj4W9f+Xh9XQeyXEuRbR13HF5AcZYqrYTO9kh1JSdb4vVXYiVZhDsSiQypZl80GqWmpgaj0UhxcXG/+6bGZur1eux2u2IBLCgoICcnZ1CvQTgcVmojSpKE1WqloKBgUBbJYDBIU1MTgUAgEdd0/kuw/NfQ+DUU7w1H/RrUo2cR8/l81NfXo1arld7eI0UyoSoej1NUVITVaqWlpUUJCejvhiHpGtdqtUqyVSqSJFFTU0M0GqWyslK08ROMa0SCi0AgQJZl/H6/EocoyzJmsxm73Y7NZhs111hqeZvCwsI061mybl48Huc7n54bX1qftu/0AhMv/PjAAbdES01g2VZiSmrR72S84GDbrsXjcbZu3Uo8HqeqqqpPq6ViuWtuJh6PY7VaCQQCxONxnE4neXl5g8ri9vv9uN1u/H4/Go1GqY04GFESi8WU4tAGgwGXyzXk7jLDgSzLtLa20tbWNujM9sGSKtotFgtFRUV0d3fT0pJo15e0yvYW3L1d433V8pRlWemqM1qtBwWCvhAJLgKBYJvIsqzEIXZ1dRGLxTAYDOTl5WG320fV0pHakq+3GzjV9WsymaioqOCV/27JmOO7ttCARFyqADKZTGkdXxo7gzz9aQ2e7gjHzXCxd7G5z6LfgyGZ+RyJRBShGIrGCUbiOCyJaxwKhZS+0En3vtfrxW63k5+fP+DXIhaLKbURo9GoYsW02WyDskamlucBBhX7OVLEYjHq6uro7u4e8W4sqeWZXC4XJpNJyba32+0UFhb2KVIjkQi1tbWEw+F+XeOyLNPY2IjP56O8vFwIRcFOgRCLAsFuRiQSUQRiOBxGq9UqcYhGo3FUBUFqUgkkimVnZ2cra0gtS5MqEKYVZSaGTC/atvdBlmU6Oztpbm5GluWMH/MWb4gTH/kId3cEgGe/qOPq/ZwsmJnfZ3brQGlpacHn8ymFw/+8bBN/WbaJ7kic/Sqd3HZEMaqQF61Wi8FgIBgMKm30BupeDQaDSm1EgOzsbHJycoYUV+rz+WhubiYcDu9wzcbhIhAIKDUpt9Vfe0dJtQomS9goxbMNhm124/F6vdTX16PVarfpGm9tbVXa+I10VxmBYLgQYlEg2A2Ix+NKokogEEClUpGdnU1hYeGgs2mHi2g0qlhYbDYbLpdLESWpXTiS5VBSf3yPm17IG9MKeWtNMwAOs45fnTSt32OlJrAkCx73dgU/90WdIhSTvLy+mxtPqRry9eno6KC9vZ3CwkKys7P5aGM7973d4z7/bKuH374V5DdHlyidbgYqhiRJwuv14vF4lNqIeXl5OJ3OIYm7cDhMc3MzPp8Ps9k86OSdkSBp4WxublbK+vRZ93EYSM2iT2bW19TUIElSWvH33qR2E8rOzlYKc/eFaOMn2FkRYlEg2EWRJEmJQ/T5fMiyrCSMZGdnj1mJjqSFr6mpCbVandHhIhqNUl9fT3d3d0aHiyRajZq/nr83axq7aPWF2b8yB5M+83wGk8DiC8cytnVHpCELxWRMpMPhICcnB4APN7ZljPuqMYgsy32WXemLaDSqJKzEYjEsFkuGRXYwxONx2tracLvdaLXaHZprOInH4zQ0NOD1esnJyRmxjiapYs9sNuNyuXC73dvNjIf0jOy+XPVb2vw88t9NbGnvZp+SLH5QrqK4IG+7mfACwXhDiEWBYBdClmWCwaDiZo7H4xiNRgoKCrDZbCNmlRkoqT2W+4r9Sia4qFSqbQq7JNOKbPRnT/T7/TQ2NhKJRAbUWeXEmUX8/cMtSCkpfyfPLh7M6SkkS6aYzWaKiooUAVGWkxmfVuowMWnSpG2uLVkIPVkbUa1WY7fbcTqdg062SZ2zs7OTlpYW4vH4DveSHk5CoZDSvnCwfbwHQ3d3d1pMajIuUqfTbff9l5qR3VeSij8c48y/fUq7PwzAN3WdbG61seiSGSNyLgLBSCLEokCwCxAOh5WC2dFoFJ1Oh8PhUOIQx5rUTitqtTrjhzi1X26yn/RQ4+RSu50k484Gcg1mlNh49Ly9+fOyTbj9EY6f6eLGoycP+vjxeJza2lo0Gg2lpaWKUJQkiUPKjEzK0bPRnXB36zUqfnni9H4FWjweV2ojhsNhJSPZbrfvkGU4EAjQ1NSk1HAsLCwcN6Vbkp1ODAbDiHVjSbUmmkwmcnJyaG9vJxaLbVc0y7JMS0sL7e3t28zIfndtsyIUk7y/pYuOQBSnZXxca4FgoAixKBCMczoDET7e1M7fPthCnSfAoVPyuf2EqVgNaiUOMRgMolarsdls2Gw2LBbLmLsRk6TGC6Z2WkmSWsduKMWmk2wvgWUgHDOtkGOmFQ762KlrWLdpK8s2dpCfn09RHCyaRBJPS0sL0WiUv5+1J6s80BmMcfieBRTbM+MCw+Ewbrebzs5OJElS3KE7+rpGo1GlRqDRaNxmwka/SBJ4toC1AAx9WN4iAfjgXti4FBzlcMjPwTVzANNKNDU10dHR0Wenk+EiEAhQX1+v9G9OZqJnZWVtt5B7NBqlrq6OQCCw3ex4dR/b1SoVmnHyuRQIBoOosygQjFOicYmfv7iKV75uJN7rY3pAuZVbD3YCYLVasdvtfffzDXbA2ldAlmDPk8GSM1rLV5ITWlpalK4j3piGGneAWaU2jFp1WqxYSUnJkK1b4XCYhoYGAoFARrLMaCHLMl98V83lz62nIxQHIC9LzwPHFePU9xTD7s/KKcsyPp9PiZfTaDQ4nU4cDscOW/0kSVKSK1QqVb81ArdL49fw3IXQWQM6Mxx+GxxwVfqYFy+Bb5/veWywwTUrICs9Tu/1VU0883kNKlSctU8Re2aFCYfDuFyuEenGklov02g0Yjab6ejoQKPR4HK5thun6ff7qaurQ6VSUVpaul2RHYzEOeKB5TR2hZRtC+YU8+BZs4frlASCHWagOkuIRYFgnPL3D7fw29e/6/M5FfD+dftSlLeNzFf3ZnjiGOhOJFX41Nl8NO8pfnD4ocO+1u5wjHfWNhOX4OhpBRhUkiLenE4nBQUF3Pv2Bh7/PiYw26jl5kMKmJmvU7qSDEUcJGswtre3o9PpKCoqGrOi0W63m18s+ZZ3N3enbT9uio37zpzTr7iIxWJ0dHTg8XiIRqOKWzTZ4m9HSArQ5uZmIpHIjpfC+dO+0L4hfduPP4GC7yNHI91wdynI8fQxxz8A+16iPHzz2yZ+/K+v0obccYSLs+btOSIZ2Kndd2w2G93d3YplMS8vb5sufVmWaWtro7W1laysLEpKSgZ8/Ro7g/z1/c1saetm3qRcLjqoEr127GNCBYIkoii3QLCT8/Gm9n6fsxi0FOblot3WD8/HDylCEcAqeQkuu4+/akq54pAJw7bO+o4Apz/6P5q9CQuK4zUtdx+VT1WuRXFzrqzr5G8f9BTS9oZiPPhRC8tvnI/ZPDRxkExgSf3RH6vkDJ/PR1NTE63BzOfcEU2fQjEQCODxeOjq6gLAZrMptRGHg3A4TFNTE36/H4vFMuDYTWIRCHvBkpu+3deSKRQBqj/uEYsqNai1EO8lFjXpltFnPq/NmOaD+hgLh1koploTDQYDFotFiWUtLy/f7vXY0ULgRXYTvz55+o6ehkAw5gixKBCMU6rysli2PrPUCsBl86u2b6HoqMnYVKZq5Q+f1gyrWPzb+1sUoQjQEYzx0oYQj+4/SxFv39R1ZuzX2h3DH1Mx2P4Vqb2jB5PAMlKEQiHq6uqwWq0cPlXPN40b054/eFKP6JIkia6uLjweD8FgEJ1OR35+Pg6HY9jc5vF4nNbWVtxuNzqdjrKyMqxW68BEzuePw39/C6FOKJoDp/0DchLvlYDKhN6YgzbkTt8nb0rP/3Um1rgWMK3+WWWTnOVCNfXktF006sy1aDTDK/SDwaDSOScrK4vu7m5isdiA42K7u7upq6sDGNFC4ALBzoAQiwLBOOWy+VW8+W0jjV2JjEqzXsMRe+Zz8qxijpxasP0JJh0FW99P27Q8PovhDjypdndnbGvpltKsfDNLMkufFNmM5GQNPNM1mVGd7M27I8kwO4osy8QkGZUsUVNTg16vp6SkhMuLYHNbN6+tSpT/OXGmi0vnVxGJRJTaiPF4XOnQMmARN8A1Ja+PJEnk5+f3mdXr9oep8QSY6srGqEtxvzatgjdu6nnc+DW8dAXSRW8rsaW5+9xIwSe/QiVFE2OmnwZVhyi7vLOmmSs2ncA5GhOHqL+hTs7HX3k51xrTX//z9y9necqNkEoF5+1fPizXIbU9pF6vR6fT4ff7t+mCD0XjfFndQaHNwIS8LNrb22lpaRnxQuACwc6CEIsCwTgl32rg0ROLWNUuY7XZOXJqAVmGQXxk97uCrvp1mNY8C8i8HJ/HY/ETuG6/smFd58GTcvlwY3vGtlTmlDm49OBK/vHRViQZrAYtd582s08LU1+EQiEaGxsJBALb7M07GjzzWS1/eHcD7u4w+5Vmcf0BOew1rRKNRoNGAw+fPYffnDwdGRmtFKG5oR6fz4darcbhcOB0OoenHEzYD2/9HNa8gmRy0jbtItqKjuy3Qw3An5dt4qGlG4jGZexmHQ//cA4HT8olEokQX/16ppW3/nM2rV1JVGVIZP9OuxLV3FNh6wcJi2PJPmnD317TgoSap+NH8XT8KABKN8O1vaY9Ys8CFv1oX/79WS0qFZy7XznzJ+94oepgMEhDQwOhUKJPePLfqqqqfnswf1XbwSWLv8TzffeeIyfZuHaujYL8fPLz88dNVQGBYCwRYlEgGKd4vV40SJy+3xDbrml02M78M19tvo1FH22hNaTml7OKOG+YxeKPDqpkQ4ufl79uQJJljpvh4qrDJmaMu/X4qVxwQAV1ngCzSu1YBiB8eyewjLU7cGVdJ7e89K3y+NNaP4+ZjDwxpycmLx6PEwt6cbvdRCIRDAYDRUVF2O324Y2pfOsX8PXTAKgjPvI/uYPsc2ZjKu07Rm5jiy+t1WBnIMpP/u8rnjy1FGSJbMlK73dG1JiDzmyjvLikR+Bmu2DWWX0eoyA7UwQXWPsOEThsSj6HTcnfzkkOjNQkFK1Wi1qtJhKJ9NlVpTe/fHm1IhQBlm7s4oSZxcwsGID1XiDYTRBiUSAYp3g8Hsxm8w4nPOw1wcVeE1zDtKpMdBo1958xi9tPnIosg83Uv8uu1Gmm1DmwKMVk0sh4SGBJ8t53LRnb3t+YiOELhUJ4PB6lNqLNZqO4uBiz2bxt61TAA131kL8naAbm7pQkCda8TOrVUCFj2vouTD60z32+ru3M2NbeHSOstTC5yIl5yqXIzW+j2voBALJKTXj+bVRUDrw39vkHlPP8inrafInQCZ1GxTVHTBrQvkMl1Zqo1WqJxWLbtK6mIssyaxq9Gds3eSJ9jB4kWz+AtvVQOT89rlMg2AkRYlEgGIeEQiG6u7spKSkZ66UMmGzj8MR1pSawWCwWysvLR6SLx1Ao6qOAdoFVz5YtWwgEAmi1WnJzc3E4HAOLc/vwAVh+D8TDkFUIZy6Gsv37HZ4shdPU1ESF3o4h4ksfYOnflTu1KLMsRo5Fz4wJpei16kRP7vl/BNe7WKUOrHMWkFUwOJHjspl467qDeenrBnyhGCfMdDGpYNstG4dKqjUxWfpGo9FQUlIyYOuzSqViVomNb+q70rbPLrXv2OKeXwhrXkoeBY67D+ZeumNzCgRjiKizKBCMIpGYBLDdTObGxka8Xi+TJ08ec2vaaJHaElClUlFYWDhmCSz9EYjEOPUvn7CuOSHS1Cr4yYG5HDctj5ycnL4Lo/dH82r460Hp2xwVcO3KRMZHL5KdRrq7u1GpVGTXvEXJ579Bxfdf4bZSuOz9bRZe/93ra/n7R1uRZTBo1Tx41mx+ML0Qj8dDS0sLarWaoqKicf99GwqFqK+vJxQKoVKpkGVZqdc52M/L6oYuLl78BS3eMCoVnLVPKXefOmPo77ua/8GiY9O3GbLhxvWgH2zuv0Awsog6iwLBOCIuyfzmtbX8+/NaZBlumtLKRXtIaCceCs7K9LHf9wMeyg/fzsp4SmBJsq7Zy20vrear2g6mFmVz54nT2CPPwCMnlfP66ibcgThH7VnA3Cklgy7dE4/HiWxYRoadsqMafM2JuMCUsS0tLXg8HuX9YDabKTjyGlQzD0l06LHkwexzt9uh59bjp3LufuVsbvOzV5kDs1Zm69atBAKBPlsxjjdkWaa9vZ3W1lZFzGVlZeFyuYbc5WZ6sY2Pfn4439R1UpBtHHCYRHI90WiUUCik/Bm++5iMaMewF7pbQV8xpDUKBGONEIsCwSjw5CfVPPlJNSDzqO4hfrDlC9hCoojxyX+G2ecoY5Mxb06nc6yWO2qkFk3W6/VjnsCSJC7JXPzklzR0Jqpsr27wsnDRZyxaUEy22ch5B07E4XAMSliFw2F8Ph8+n49AIIBJclLVe1BWgeJKlmUZj8dDa2srkiQp4qikpASbzZZ4XLJPRkby9qjItVDmNNHe3s6mtrZxkTg0EFKtidDjch4OK6hOo2afim1/3iRJShOFoVCIcDhM/PsC5Gq1GqPRiKHyEOTP7kKV2sXGWQX24SkNJBCMBUIsCgSjwLJ1rQAcqF7DDzRf9DwhS/DObTD9dNDqFYGQnZ29y9d28/l8NDY2EovF+q0JOFasbuhShGISX1iiVbax96SyAbkoJUkiEAgoAjESiaBSqbBYLBQWFmKddAZ4P4Wv/pnYQWNIxLZptHR3d9PU1EQoFEKj0SDL8rBZXJOt78LhMLm5ueTn54+b694XSWtisr4mQF5e3oglPPVlLQyFQkQiPUkver0eo9FIVlYWRqMRo9GITqf7/n1RlbgBfOdWCLghdzKc+nifoQUCwc6CEIsCwShQ/H1ixARVY+aTATcEPWAtpLu7m3A4jMs1ctnLo004FmdlbSeFNiPlORai0ShNTU14vV4sFgsVFRXjJoElSZ7VgFoFUq+I7ooCxzaFYiwWU8Sh3+9HkiS0Wi1Wq5XCwkKysrLSBc5Jj8B+VyT6eJcfSESXTXNtLV6vVxGFarWa0tLSHbb8SZKkFNc2Go1MmDDEkkyjSDgcpq6uTrEmms1miouL+32/yLJMNC4PuP9yX9bCUCiUyDanx1qYKgqNRuP2RerssxMFywPutJACwQDoqof1b4I5B/Y4HrTj67thd0WIRYFgFLji0Am8+10LnwSmIckq1KoUFZK3B1gLgUS5nGQP212BlXWdXLL4S9r9ieSBk2fkc+ksM2q1Ot2dOs4ospv44dwynvmsp4fxD6YXZmQUy7JMKBRSBGIwmLBGmkwmcnNzsVqtGI3GbZ9jwTSkvD2/rye5EbVarZSAGS7LX6oVt6CggNzc3KFfdykO6pGNa+xtTdRoNLhcrm2+X57+tIaHlm7A3R3h8Cn53HP6THK/7xA0GGthbm5uH9bCIaDVC6E4WDa9B/8+O1EdACB/Glz0FhjHd8LV7oAQiwLBKFCZa2HpTw7h9VWT+Kymg/22/gl12As5k+C0vwMQjUbxer24XK6xF1DfvQof3Afdbph2Chxx+5Du8G996Vva/YkvflmGl1e1clB5FQv2mzTmCSzb47DJeaxv9uIPxzl5VhGXf99POx6P093drQjEWCyGWq0mKysLp9OJ1Wod8LnJsozX66W5uZlYLIbBYCAUCmEymSgvL99hy18sFqO5uZnOzs4dt+JuXJroGOPeBGUHJqyiuZnF1wdLdzjGs1/UsanVz0ETczhyspO6ujrC4cT7xul0UlBQsM340BU1Hdz28mrl8XvrWvnp/33F735QPnzWwuGmfgWsfRnMTph9HmTteAebnR156R2okkIRoHUNrPwX7P/jsVuUABhhsfjBBx9w3333sWLFCpqamnjppZc45ZRTRvKQ45b6jgAfbWyn1GnmwAk5Yy8GBKOO06Ln/AMq4ICfQ/Ra6G4HW4kSy5TMdrXb7WO6Thq+gucuSMRTAvzvTxCPwnH3DmqaWFzqs+BxXUAz7oXiiyvqufH5b5THD7VvZHaBDpcpEYcoyzIGgwG73U5WVhYWi2XQn+lgMEhTU1Mi2cVkQpIkIpEIhYWF5OQM/jvi69oO7nlrHZvbujmgysn1h5QS7mpHluUd76Ptb4P/OxdiCXcwtZ/Ac+fDlf8b2nzfE4tL/PCxT/m2IVHn8N+f13LyHlYu3ceJXq+ntLR0QIL5v+syi6V/sMlDd3cuBoNh+KyFw8W3L8CLl0Cy7NFnj8Hl70PW8HS02RmQJIlwOEwwGFQEfbl7Cxm3BJ6tY7E8QS9G9Bu7u7ubWbNmcdFFF3HqqaeO5KHGNf/5ppEb/m8l8e8DoA7fI5+/X7AP6gH2xRXsguhMYC9VHkqShMfjwW63j33pktUv9gjFJN8+P2ixqNWo2dOVzXdN6YJxVoltR1c44iz6JP0HKhKTePrTGn52eFkiOcVqHXKpllgsRmtrKx6PB71ej9lsJhAIkJWVRVFR0ZDm7QpEueAfn+MLxwD4zzdNbG7y8Ojpk3G5XDuULCVJEpE1r2NMCsUkrWsTP+S9Sj8Nhg82tilCMcnrG3xcf+RkKooLBizqXLZMQVnsMDFp0sh2jxkq8vv39NTHBPA1wleLYf5Px25RI0gsFktz/weDQcVyDGAwGDAajUTL56PZ9Eb6zhOPGOXVCvpiRMXiD37wA37wgx+M5CHGPXFJ5revrVWEIsB/17WyfEMrh+8heo8KAEnC29VJPB4fH+VyjPY+tg1N4P1uwXQuWfyl0nv39L1LOHyPUbCe+Nto/t+/6QrFKZl3DhbH4D5r0VhmrwKLNZuKioohLymZ6Z6Mw8vOzsbn8xGPx3c4fvO/61sUoZhkTWsYnS1v0EIxHo8TCATo7u4mEAgQDAYxd6vIkIRaY8KFOkjWN/v49+e1ROISuVmZwjgmgdE6uGuxYE4xT/2vhvUtPcXSbzpmj0GvbbhJWs96x0pO8rZm/vh2t4/FEoeV1NjQVIthNBoFEh1zjEYjFouFnJyczBCAUx6GJUHYsgz0WXDgtTD5mDE8I0GSceULCofDaXcbXm+mC2tnwx+O0eoLZ2xf39glxOLujizDe3fC54+THY9SNuEkjHv8ZaxXBXPOg8/+CoGUH695Nwxpqr3KHHzyi8P5qqaDQpuRqryRr+UnNa8l+NjRFEo+CoGOFQ+w6ZSXmDV73wHPccY+Jfz29e+Ux2oVnLFP2ZDX5Pf7aWpqIhwOk52drcSnDlc5nL5aLeo0Ksw6LQ2dQd5Z04zDrOfY6YUYdemW61Rx2N3drSTpaDQapcyPpepM5PqXUG1Z1rPjQdcN+iZidUMXpz36CeHvOxmpAYNGRTjeI873KXf0aSncFhaDlpevOojXVjXS6gtz5J4FTCkcmTaDfSHLcob1LFmHMYlOp8NoNOJ0OolPOR7tt/9Kn2TPk0ZtvcNBbyGcFIfJ2FCNRoPJZMJms2E0GjGZTOj1+m3fBGTlwQUvQ7ADtCbQDa7YvWDkGFdi8e677+bOO+8c62UMKzaTjunF2axuSBe+xVo/tbW15ObmYjaLFlDbIi7JxKWBl8PYaVjxJHz0IJD40cze8Dx8PBkO+dnIHnfrh/D5YyDFYM75sMdx6c9nuxLxU18+QaC9jra8gyidcz5DvfpGnYYDJ+bu8LIHSvMbd1Ek9fRMduDjs9fvYdbsFwY8x8XzKtFp1Cz5qh6zXsslB1cyt3LwVrRIJEJzczNerxeTyYTD4aCzs3PYC2EfMjmPqa5s1qa4/M+ZW8aqhk4uXvyl0mZy4rIsnrt0Llo5qojDZFkarVaLxWLB4XBgsVgyf9jPfT7RLaZtPVQeDJXzB73ORR9XK0IRQAIm5JmwGA2JWMsJOfzqhKlDugYmvYYz9ind/sAdpD9rYe/i3BaLBafTqVjP0sJLTrwP9DpY/VLCOjv/p1BxUD9HHHvi8XiapTAphJPdgpOZ5Hl5eWmxoUPG5BimlQuGi1HrDa1Sqbab4NKXZbG0tHSn7w29scXH1c98zfoWH1aDlhuOmsQpU+20t7cTiUQwm81KmY0xD7weZzy0dAP/+HArwWic42e6uGvBDCyGcXWPM3T+dSZsfDt9m2t2QqiNFNUfweKTILW7xBlPwrQFfQ4Ph8Ns3LiR4uJiHI5x9gW+4kn45v/AkAUHXAVVhwLQ8MB8in3fpA39OD6N/e74CK1mdG444vE47e3ttLe3o9FocDgcdHV1EYlERqygtC8U5d+f17Kp1c+BE3I5eXYRJ//5Y1bVp8cEXrSXnVOn2tDpdFgsFsxmc9/icAS4/KkveXtNejLKrFI7r1w1/oTSQKyFSZGU+jcuEmiGSO8SQ0mB2NuNnPwzmUwYDIaxj7MWDJmdsje0wWAYd8V5h4NJBVbevmE+jZ1BnBa94gZyOBz4fD7a29upra1Fr9eTm5uL3W4f1x0VRovXVjXy0NKNyuNXVjbiMOu546RpY7iqYSS7KHObrWRkj/nlE+lCEeDzv/crFpM1Hzs6OsaXWPz0r4kyLkk2vQcXvQ2l+xKpOgK+SReL31kP4KBREIqyLNPV1UVzc7MSgypJEm1tbZhMJiZOnIix9n344u1EgtNeFw4p7q8vrEYdl82fkLatzhPIGOeTDUyePHnICTo7woI5xRliccHsPj4Ho0xqZm6q1bAva2Ey1m5nF0myLGdkIweDwTQ3stFoVNzIyXPeWYWwYMcYV2JxV6fInh6Ho1KpyM7OJjs7m0AgQHt7O42NjbS0tJCTk4PT6Rz3JUZGkv9+15qx7b11LbuOWDzwmoRbL+hJPNZZ4OAbR/aYUryPbbHMbSk0h3X84d0NtIVqOHhSHj89dkqfMXKjyoon0x/Lcfj6KSjdl8qTbuHLhs3MaHsdUPGa5gj2P/uWEV9Saimc7OxssrKylL7OLpcLp9OJ6qMHE3GqSb56Ci7/IGEdHQEOmZzHyyvTuwYdM6O0f6EY6YamVZAzYUTKuBw73cXvT53Bk59UE4lLnLVPKRceWDHsx+mPwRTnTk3A2JmthZCwdPe2FvblRs7NzcVkMmE0GtFqtTv1OQuGlxFVIn6/n02bNimPt27dysqVK3E6nZSVDT1YfFfEbDZTVlZGOBzG7XbT1tZGW1sbDoeDnJycXdLiuj1c9szgZlf2LhTwnDMBrvo8UZZGiibag420ZXGvCxICNbVsxz4/6nd4R3eEy55dgy+UEJTV7hoaO4P8Y+HAk0WGBSkOXz8NW99PFDKnj+gZ9fdfZxod+1z9T5rcHbT6Ipxcmjei7udYLEZLSwsdHR0YDAZKSkrwer00NjZitVpxuVwJcRaPwccPpe/s2ZwozDznvBFZ269OnEZXMMryDW1Y9FouPbiKI6f2k1i3/i1YchmEu0Ctg8Nu3qGbl+5wjDv+s4bXv23CYdZz7RETOWvfMn44N/G3I2xu8/On/25iS3s38ybmcPVhkzDp0618I9bKbxzTlxgOBoNpbmSDwaDEz/YZTykQ9MGIxiwuX76cww47LGP7hRdeyJNPPrnd/QfqS98VicVieDwe3G438Xic7Ozs3S4ZptUb4pQ/f0xjVyIAX69R8dujXJx8wNTdUjwPF/G1rxF4/4+YdBq0cy+CmWf2O/a5L+r42Yur0rapVPDVbUfhsIyiG/PV62HFIuVhQJ+DOeLueV6jh0uWgmvW9udqW5+oJam3wKyzh2xBS9bGbG1tRaVSkZeXh0qloqWlBbVajcvlIjs7W7HOxEN+1PeUoupdw/Ko38BB1w5pDQPFH46h16j7TxKLReDBqdDdlrJRBVd/Abn91CrsrAXPFijeGwyZmcc3L1nFvz+vS9v23OUHDClRKBVvKMrh9y+n3d9jDTx2Wj73njylX2thso5fUigZDIbRsxY2roQ1SxKZ47PPA+u2q2Bsbe9mTWMXs0rslDr7/75PupF7l6lJus6TbuRkbKFwIwv6YlzELB566KGMUv7MLodWqyU/P5/c3Fw6Oztxu91s2bIFk8lEXl7ebpEMk59t5K0b5vOflY10h2McvWcesa4WtmzZQkVFxQ63QttdCZUfRs3BFUycOBGtcduW2t7WGgCdWo1uNDPTgx0JF3MK5oibRdLxnFoWwGZ3wn4/HphQ3LwM/nVGwpIL8MkjcOl/wT44S5fP56OpqYlIJILT6cRms9HS0kIgEMDhcFBYWKhYa+LxOB6Ph/b2doqLDia7ISWBSaOHPU8c1LGHQtZ2ksJi7s1o04QigAz1X/YtFpfeAR//MVG8XW+F0/8Bk49BlmUikQihUIjXVzVm7PbW6ubti8WuBlh+NzR9AyX7wmG3gKUnm/7dNS1pQhHgnbWtXDhVj92ccKcme3InBdKYWQvXvQ7/d35PnPCnf00ksPUVr0wioe+P721ElhPlmm49fioXz6tMcyOnFrVO/r7qdDpMJtMu5ToXjC9234C4nQS1Wo3T6ewzGSYnJweHw7FTu022R7ZRx3n7lyuPY04z1dXVbN26lYqKit3K0jpchEIhxR21PY6aWkBFjplqd0+ixA/nlm5XfAwrsUifcZWrYmV8pD2Nf5w+CJf4B/f3CEVIWNI+fwyO/u2Adg+HwzQ3N+Pz+TCbzZSUlODz+aiurkan01FZWYnFYgF6LI+Bb1/Dtvk/lBuM6A+6AjaUwIbvE1wOv22HOqDsCLIs4/f76ejowN8ZZLLehjaSnjlN0ezMHRtXKiWfAIj4iL98NdULXiMcjStuXrtBjTeUHiOba92ONVqKwz9PBvf3iW3Nq6Dxa7isp76jpo/OVypg8qRJOK2m8SWQ3r83PaGsuxW++Acc8cuMoXWeAA9/LxQBJBnuefM7ZmaHMKkTcyQ/t0ajUbiRBaOKEIs7CX0lwzQ1NdHa2orT6SQnJ2e3SIbRarVUVlZSU1PD1q1bKS8vH7ZadbsL4XB4wGVSjDoNL/z4QBZ/Us3W9m4OnpTLGXuPfC27NKwFyFWHpRWE7pQtvCftRa67e1BTyf5mMs7al9lXuDfxeJy2tjbcbjdarZbS0lI0Gg0NDQ2Ew+G0cjiSJNHR0ZHIgK5dTtknv+hp7bblLbjwP3DKIIuvd1TDWzdD7adQMA2O+d3ALKl9EA6H6ejooLOzk1gshsFgIL+oDNWJD8ErV0IsCCo1zPsJ5O+ZOUHjVxmbNIFWzPEubPlVioD5meTk2n9/TbJ5VbHdxFnbq4NY80mPUEw9XvO3UDgDgKOnFeCyGWnq6mk/ePKcYnKyx8eNoyzLBINBvF4vOV1NZKSCZVhwE2xq9SP1csRF4jKeqJa5VYVKUetd2TggGL/s+upiFySZDBOJRHC73Uo9N7vdTm5u7i4fz6fRaKioqKC2tpaamhqlVZpgYIRCIYzbcT+nkptl4Majp4zgirZP+6H30tR1O7a2FWyWi3ggdiZeLJw6KW/Ac8iyjL/kUKzuTelP7HnCNvfp7OykpaWFeDxOXl4eDoeD1tZWOjo6esrhGI1pMYyxWAy73U5R4xvpPYDlOHz+OFTMG/jJyzI880No+76jTPWH8NSpcP23oB+YQIrH43R1ddHR0UEwGESj0WCz2RTrlEqlgtxTYeJhUL8i4Xp2lPc9WfHemdss+bgm7QWanp+UE2YWUe608MbqJnIsek7bqyQtzvXNb5v4vy/r0GvUXHhgBQdUOfH5A/T5SVb3SC6zXssLPz6Qv72/ma3t3cybmMuPDhob62ySeDyO3+/H5/MpLRw1Gg2WqqPRrU4PoWDqyX3OMbPEhl6rVgqoA1gNWuZNr9x1assKdlrEO3AnRq/X43K5yMvLw+Px4PF46OjowGq1Kskw48olM4yo1WrKyspoaGigrq4OSZLGVx3AcUoyKH5nssbGYjHa/DFyTvsDj3/ZwTOf1xJD4phpBdx0TIqIbf0OogEo2iuRhZOCJEnU1dXhrzqXCVII47qXEgkuB17T7493IBCgqb6G7BV/YkLTh2hsLoL7Xs1mz6S0cjgAHR0dtLa2Eo1Gsdls5Ofno9PpiEdCmZ1v4tGMY22T1rU9QlFZXDts/QCmHNvvbrIs093dTUdHB16vF1mWycrKorS0FKvVmmmhkmX47lVY90aii88BVycy9nvjmpXIkv7wQRI9WEi4Vx87FM5+Ji3+c0aJjRklmfLvlZUNXPfsSuXx0u9auPtoF9NyizDlTkXfvrZncOUhkJ/e57nYbuLXJ0/v99xHg3A4rIjD7u6EhTvZzs9qtWIymVBNvB9MhkTFA6Mt0TZz4hF9zpeTZeCe02Zw+8tr8IVj2M067jltphCKgnHBqHVwGQq7czb0UJAkia6uLtrb2wmHw5hMJnJzc9MyMnc1ZFmmsbGRjo4OCgsLyc0dvbZyOyPRaJT169dTVla203ymGhsb6ezsZPLkyWi1WgKRGNG4jM30vbUpEoD/Oxc2/zfxOG9POO9FsBUDCbFZU1NDKBSirKwMq3XbPYOj0SgtLS10dnZSsuoh7BueV56TVFqaTnmB/Knz0Gq1dHZ20tbWRiQSITs7m/z8fAwGgyIesza/RskXv0k/wNnPwpQfDOjcJUmiq24t9kXz0i2UABe/C6VzM/aJRCKKmzkajaLX63E4HNjt9m23YHvvN/Dh/T2PTU646rP+s8U/+yu8+fP0bVOOTwjG7XD6o5/wZU1H2rajpzj407n7oI93JxKPmr6BkrmJ7jwjVIdyMCTFd1IgRiIRVCoVFosFq9WK1WodlkLngUiMGneAylxLRh9vgWC4GRfZ0ILRRa1WKz8Kfr+f9vZ26urq0Ol05Obm7pLJMCqViqKiIjQaDc3NzUiSpJQwEWSSbFW2s4QqhMNhPB4PBQUFSkyuWd/ra+vzx3qEIiSscO/9Gk79G5FIhOrqauLxOJWVldtMiJIkSalxmnxf2f7zZtoYtRyjqP1jvIG9aG1tJRwOY7VaKS0txWg00tXVRW1tLZFIBJvNRt6R10BxUaKIuFoLcy8dkFBMjXuMxUA/6SQsG1/pGVBxcJpQTN4odnZ20t3djVqtVtzMJtMAkj5kOXEdUwl6YNVzcODVfe4Sb/6ODClT+8l2zw36rJKJwWj6Xmzp4YjbBzTPSBOLxdLcy5IkodVqsVqtFBYWYrFYhie5JBZJtP4M+zFPPoY9XcPT1UcgGC6EWNwFUalUyp1uMBjc5ZNhVCoVBQUFqNVqWltbicfjFBYWCsHYB8lM6LFo9TYUWlpa0Ol05OTk9DtGqv8i09XbsIJgMEhNTQ1qtZqqqqp+BbIsy/h8Ppqbm4lEIuTk5JCfn08kEiGMnt7RndXtAbrr6sjKyqK4uBiTyYTP56OhoYFQKKSIR6W00+xzEn8DIF0kxhSXtmHqIvj2Baj9HxROh9nnIssygUCAzs5Ourq6kCQJi8VCcXExNput58awdV2iGHhXfUKo7ncFqDVpx/R2dZEdi/ThMk8vUZO8Vh0dHehkJxkFYPKnDug8z92vjBUplkW1Cs6eO8qJU32QDNNIisNAIFEFINnRJTs7uyfGc7gIeGDRD6BtXeKxwQYXvAzFew3fMQSCHWTXUQyCPjGZTJSWllJQUIDb7VYSYna1ZBiVSkV+fj4ajYampibi8TjFxcVCMPYiHA7vFIV5u8MxYpEQXq+X4uLiPi3ikUiE9vZ2NNoSepc5bsuaTNvWrRgMBsrLy/u9OQqHwzQ1NeH3+7FYLJSVlaHX6xXX95eak1jIkz3zytksDs3jZ1VVmM1muru72bp1K4FAALPZnFY6ZzD0Fol2u528vLz0z+ess2DWWUSjUTo7O+noqCMSiShi2uFwZN4E+JrhiaMh9H1JnOoPE6Lx2LuJRqNKnHMsFqNs4klkr3+uZ1+dGWacrlzrjo4OZazRaMR64KXI7k9Q1X2aGG+0w9G9XO79cOpeJWg1ap7/sg7d9wkuB04YmxASSZIIBAJ4vV58Ph/RaBSVSkVWVhZFRUVYrdZtu+93lC/+0SMUIdFB57+/hfOXjNwxBYJBIsTibkIyGSY/P1/pDLMrJsPk5OSgVqtpaGhAkiRKSkp2Odf7jjDYTOjRxtMd4cbnVrJ8QxtmrZoT97RzRpbMtKy4Er+VtJZ3dXWh0WjIPeAK3E1fkONeAcBWqYCFG4/m5mkqjt6jss/XPx6P09raitvtRqfTKbGMfr+fLVu2KO7Gf+kW8L8uB8dovqBVtvPP2NHMVBegUqmorq7G7/djNBqVEk6D/QwNSCR+Py5p0fP7/ahUKmw2G0VFRVgslv6Pu/rFHqH4PfKXi6jb4zK8/oS72m6343Q6Me7xZ/hoIqx/A7KLkA++EZ/aTkdNDT6fT3FtO53OHqvpRW9BzccJ69iEw/rs5NIfJ80q4qRZfRenHmlisZhiPfT7/UiShE6nUzwyFotlVL43ZFkm1rI2s7xO+0bwt8Jbv4AtyyFnIhx5B5QfOOJrEgj6QojF3QyNRkNeXh45OTlKMszWrVt3qWQYh8OBRqOhrq6O2tpaysrKhGCkx8U2nhNb7nx1DcvWJ+rQdUclnl3l4dlV/8Np0fPAqXtSaUnEkOl0OlwulxKHe4but4TCKzAT5gt5ChJqltaEOXZu+usuyzIdHR20tLQgy7LSJUmWZaqrq5Ws1tzcXAoKCjiqGv6yfF/elnoKf19YoGXz5s0YDAZKS0uH9JkZiEiUZZlQKERHRwddXV3E43HMZnMiltJm226sXDgcJtTVlVGKRpYlwuEwLpcLu92ePs+hPydy4A09VsTOWoxGY//HVKkGVwZojEhey6RADAaDAGnfe6NpcZckSenMZTLvQUZH+Kr58MJFCUswQMANT58O130DWQMvFyUQDBdCLO6m7OrJMNnZ2ZSXl1NbW0t1dTXl5eW7fZeDaDSKJEnj2rK4bF1rn9s93RF+8dIa/nlmpVJXM/WHPRKT+FauStsnHEtPo+ju7qapqYlQKITNZqOwsBCtVktHRwdNTU3IsozBYKCsrEwRbdceMQm3P8KSr+vRqVWcMCWLQ8oMFBQUYLfbR0QkxmKx793MHYTDYbRaLQ6HA4fDsd2wkWRXFrfbjd/vR583jyzdn9FE/T3zzzqPiZOnpK09NRaxXyvitmhcCf/9Dbg3JUrdHHkHmMc2SUOSJCV72ev1EovFUKvVZGVlKeVtRjt2OxKJKK7/eDyO1WrFfsiPkVVtqFY8meguVHUoHHgt/LlXpnu0Gza8CXtdMKprFghAiMXdnu0lwzidzpGN1xlBsrKyqKioSGsPuCsl9gyWnSETutRpZk2jt8/nWvwxHIVl2LMzxe6Z+5byTX2Pu1WlgjP3SdhrotEozc3NdHV1YTQaqfo+3jAcDrNp0ybC4TAqlUqpm5gqojRIXHdgLudOUaPRaCgsyB/SjVSyYHd7ezvfNnXTGtZy6LQSSkoSiTu9xVryc1lYWDgg93Y8HqejowOPx6PEMRoMBsI4qTn8b7i2/B+GUBvqPY5Dv/+VSh3KvmIRB2q5VAh44J8n9bi7O6oTcZFjEHMXjUbT3MuyLKPT6bDZbFitVsxm88Bfu2Bnogf2lmXgrILDboOSPgqSb4dkIpLb7cbr9So36jk5OT0xpsffn2gBGA2BtQDCPtAaIRZKn8wksqQFY4OosyjIINkZpqOjA1mWsdvtSoP6nZFQKER1dTVqtZqKioqdJhNYoaMm0fLMNSvxozVIJEnmiY+38spXtRjVEj85biYHjFEywfZ4f0Mbly7+kkhcynjOZTPy0c8P77M3MMAzn9Xy3Jd1GLRqfnRQJUdPzae9vZ22tjbUajWFhYXY7XYAWltbaWtLuLstFgulpaVpNxKxWIz29nbcbjdqtZrc3FwlHnYwpIrEWCzG377y8epaj/L8z46eyII9s+ns7CQejys9f20224BubMLhMG63m87OTiRJwmAwEIvFFJe10+kkOzs7bd07bEXszcpn4OUfZ26/aWP/NRqHiWRrvaRADIUS4spsNis3wUN2Lz9zFmx4q+ex3grXrQTLwD47yXJGbrebUCiEwWDA6XRmuv77493b4eM/9jwumJHoka3ZOW/eBeOTgeosIRYF/RKPx5VkmFgstlMnw4TDYaqrqwGoqKgY19a1ND55JPGjIUuACg6/DebfNKgpHlq6gYeW9vTb1WvU/Oeag9ijcHx+puo8Ad5Z28KydS18tMkNgEWv4ZFz5nD4Hr3znjORZRmv10tzczPRaFQphaPRaJRyOkmXZElJSdp3SzweVyoGQCJhKjc3d9AhDL1Fot1uxx03cvKjn6WNM2hUPH1mGSX5OUrrvYGcn8/nw+Px4Pf7UavV6HQ6xUKaTFjpLfx6WxFzm5aRu+kFNCoJ1ZzzYb/LBnWOCmtfged6uUbVOvjpJjDZhzbnNojH43R3d+P1evH7/cprmRSHWVlZO+5BCHYg31OZWQj9xD/C3gu3uWsyy9zj8RCPx8nKyiInJ2fQCVDxeJyGpY+S512NqXh6wv1sHJ+fWcHOiyjKLdhhdqVkGIPBQFVVFdXV1WzZsoWKioqhWVFGE39bori0nLSyybDsLph1ttKdZCA8+3ld2uNIXGLJVw3cctz4/OEpdZq5eF4lF8+rZEubnxpPgL3LHWQbt29RCYVCNDU10d3drYQhGAwGpd1fV1fCVWqz2dJK8ijirrEGWYrjKCglLy9v0KKjL5GYjEn8ZlVTxvhwXMacW4LLZd/u3H25mnU6HdFoFFmWKSwsVJK7kvRnRcz1fInh49t6Jn/zp4nai/tePKjzBWDysZAzCdw9NySfO09gD5WF4XqHRSKRtNZ6yfhSu92uuJeH47so2aWls7WVIrUOlZReZxJ9/51kkq7mrq4uJcs8JydnyDemXq8Xb/GhFB52Gexs3pCR5KMH4fO/J/qs770Q5v8MduL4+p0FIRYF22V7yTADdquMMTqdjsrKyrQYxm119Bhz2jdkFEVGjidqsg1CLGo1mT+i/blyR5RYBL77D3TWwMSjwDVzu7tU5WVRlbf9Vm+xWIzW1lY8Hg96vZ7y8nKlrZ/X66W+vl4ph1NWVqa87sns6LaWJvI+u4spNW8BMqoZp8OJDzPQr8i+RGJ+fn5ayMO+lQ70GnWai70g28CU7Vh4Q6EQHo9HcTXr9XrUajXRaBSr1UpRUVGG1Wq7sYgf35x5oJXPDE0sag14z36Nf/3pNorj9XwkTef5+kM47NmVPLFw3+3v3wdJ93Ky9mEy3tZisVBQUKC4l4eLSCSiJBUlWySGZpyD+ZsnewY5q2CP49P2kyQJr9eL2+0mGAyi0+n6FO1DoaurC7PZvPOFzYwkX/8rEUeaZPndifqe+18xVivabRBiUTBg+kuGaWlpUTrDjPdkGK1WS2VlJTU1NWzdulWpjzcuKZyRsGREejJZZa0RVdGcQU1z4QEV/O6N75THZr2GM/cZ5W4ZsQg8eTzUf554/N5vvnfpXbhD08qyjMfjobW1FVmWKSgoUGILY7EYdXV1GeVwVCqV4qpuaWkhEolQXLMER/VrPROv+r+EODj0F9s8flIktrW1EY/HcTgc5OXl9fkDn281cv+Zs7jzP2twd0codZr4w5mz0WoyrSJJi6Db7Vba92k0GiRJIh6PK8lnqccZTCyirDORcbugG7ql/Z2aGPeEFqRtW7a+Fbc/TE7WwERdPB5Pa60Xj8fRaDRYrVby8/PJysoa1pvSpNDr6OhQrnF2djYOhyNhqZz4IFTuD5vfA+cEmHuZco1isZjiao7FYkpBd6vVOiwWzmSbQZfLtcNz7VKs6SNpas1LQiyOAkIsCoZE784wydhGm81Gbm7uuE6G0Wg0VFRUUFtbS01NjVIrb9xhzIaT/wyvXguhLuI6C21zbybfaM9sy7YNLp1fRa5Vz+urmrCb9Vx0UCWVuYPvMrIjyOteQ5UUioktiVIrc85Laz03GFJL4djtdgoKCtDpdMiyjNvtpqkp4fZNLYeTFFQtLS2EQiGysrISfZ1XfJl5gE1L+xWLgxGJqZw0q4hjpxXS5g/jyjai7mXhTbqa3W430WgUrVaLRqMhHo+j1+vJz89Pb+XH4DOaZVmmvfJUcr59EbUU/X6rCg64aptr3xZGXeY7UqtWodOqWd/s4/OtbiYVWNm/Kr1tY2prvaSoNxqNSmmbAfW1HiTBYDCjdmVxcTHZ2dnp10ulgtlnJ/5S9k26moERS/5LDZcQJEiEHxjJuLU3998KVDB8CLEo2CH66gzT2dlJVlYWubm52+4uMYao1WrKyspoaGigtraW4uJiHA7HWC8rk2mnwKSjwf3/7J13eCNnvf0/6s1qltzlvn2zyabtpvdGOkmAUAIk9JILhN7LpVwu/IB7uRBagCSEECCE9EB6732z3fa6q/deZn5/zGpsWXKXvfbG53n2WevVlFej0cyZbzlnLxlDM/4hNwqfj4aG6Rs9xuOth7t46+Fl0r+zwl5vnBf7g6xttLC51TbpckXx73Q6TTqdJpVKYdzzYpklHwkf5FKgm11kN5vN4na7iUajGAwGWQoHJPIxMDAgN3s0NjbKcjiJRAKPx1NizafX6wmFQqSVtZR9+xU6z+dKEsdDq1bSYiuN4qXTafm3U5R7USgUFAqFkuhg8bc0145mURQZGRkhpG5B+/Zbse7+OxRysPnd0HnijD/DRJyxvoEOh5F9gaQ89rajWvnr84N89+6xqPZFm5v53vmrZYKYzWZRKBSYTCaampowm80LknbN5/NEIhHpu06nZ61dWUw1J5NJNBoN9fWShNJCSXFFIpHqNOoscxRrSH0+H4lEAvOad2LqfxBFXhJVR6WD4z91YCf5JsFKN/QKqoqiXITf7yeTyaDX63E6nWUiyksF8s0zFKKpqQmHY2k/pXq9XrxebwlBWgz87vFevnfPDopXi3dvbeN7b91EoVAglUrJxDCdTpPJZCheVjQaDXq9HlNyEMct55d2l7afAFfePeM5CIKAz+eT/KBVqhJhbFEU8Xg8chfzeDmcVCqFx+ORrfkaGhrQ6/UlHasOVZzGu65AkdgvCm50wJX3Qd0aed/zJYkTUSnVXEyfazQaamtrywhJpSiiw6jCkhpA1XgImCY/f0VRZHh4mHA4vCAPR/54hj882UevL8EJq52cf2gzx3z/QVK5QslyPzmnkQ2NppLu5YUwACgKlBcJtSiKWCwWuSlmJtqVxXPE2HMXds/TaBztaE+8GoW9o+rzLSKbzbJ79+6l+wC7CCh+dz6fj2QyiV6vp76+Xvregr3wyk0gFKRmv/p1B3q6yxor0jkrOKAo/tj9fj+JRAKNRoPD4ahK4Xe1MZ5o1NfXU1dXtySJLUhz7e3tJZ/Ps2rVqkU5lpFUjq3ff4B0rlT78NqLWmk1Szd5hUKBTqdDr9djMBjQ6/Xo9frS+b1ys1ScHndDx4lw8bVgm752crwUTj6fx+FwUFdXJ287mUwyMDBQJoeTTqfxer1Eo1F0Oh319fUlJBGQa221Wi2ko1IDjijA+gvAYEcQBFlKp1okMZ/Py13NxVSzIAgIgoDJZMLhcJSQmSmjiLtug7uugXxKirKc/T3Y8qGKx3BoaIhIJILL5ZL1JidiJJyiP5DksFYrRu0kUa2BZyEVgs6TQDv5A8teb5wzfvJo2fh/v3UDb9vSsWC/sSKhDofD5HI5dDqd3KA3k0jd+CgvgKvnJqwv/WJsAVMdfPyZGestzhY+nw+v18u6deuW3LVyoVE8130+H6lUCoPBINerLtVr8nLHinTOCg4oKjXDuN1u2RlmKTXDKBQKGhoaUCqVeL1eCoUCjY2NKIrPUUtIlkGhUOByuejp6WF0dBSXa36p5ZlgJJwqI4oAgZyaY13N6PX6mQkfb34nHPoOKGRm3EyRSqUYHR0lmUzKjibFtKEgCAwPD5fUjzU3N5PP5xkaGiIcDqPRaGhpacFgMOD3+xkaGioR2S4hD3qLVEO5f9uB/VHMapHEIgkJhUIA8r4FQcBut1NbW1uSEp22FjEVhrs/KxFFkI7rfV+G9RdSMNXz5+cGeHSXj/ZaA2/p1qMXUrS2tk5aB/fD+3by60d7EEQw69X84l1HcNKacT7EuTT8+W3Q95j02uiA9/wDmjdX3F6X00SLzcBwOCWPaVQKTl7fVPUbf6VmFavVit1un1Hd48Qor1qtpq6ujlq7HfWdfypdOOGD1/4Kx368qp+hiEgkgtlsflMRxeIDoc/nI51OYzQa6ejomF8Z0+Dz8Mj3ITwglfKc9jXQLm6t9sGEFbK4ggXH+GaYYlRnqTXDKBQKWbh5dHgQ85Pfw7TrVqlj9Mgr4az/nLoRI9ADKu2MImXzhU6no7GxkZGRESwWy4JH3VfV11Bv1uGNZeQxjUrBWZu7KlrvTQmlEpTlRDGTL5DIFKg1SWQsn8/j8XgIhULodLoSKRyoLIej0Whwu92EQiFUKhVNTU3o9XoCgQDDw8Oo1WoaGhqmjG4XU49+vx9BEGSdxLmSxOJNMBgMlnQ1Fzt9iw0rxfnMqhbRuwNyydIxIQfu1/j29iZueLpfHr7jZRV3fnzrpETxtaEw1z7SI7+OpfN84e+vcv9/HCvLLKlevh5dkSgCJAPw76/B+++auDkAlEoFv3j3EVxzyyv0+hM4a7R8/fwNNMz2nJkERXmdYrNKMTLb0tJS1gQ0GQqFAuFwmEAgQDabxWAwyJFphUJBNBLGnE2VN5TlU5U2NzMEekBngZq6sreKtb51deXvHYwQRZFIJILP5yOTyWAymejs7MRkmiepi47ADRdJftogeZbHvXDZdfOf9JsUK2RxBYsGrVZLY2MjdXV1hEIh/H7/kmuGcTgcGF65DuO2G8cGn/kFWF2VIwmJANzybhh4Wnq97ny47PegXliHGLvdTiwWY3h4GIPBsKBRWo1Kyc/feTjX/PVVhsMp7EYN37xgI/Xjb/qBnv0eut3QdYrsPTwT/PHJPn5y/26i6TyHuax85y2daDJStLCxsRGHwyGfF5XkcJxOp2zNp1AoqKurk0ni6OgoWq2W5uZmbDbbpARiPiRxJJzCH8+wsdkqE6tKqWaFQoEgCPTElNyzO4moSHP5Fgun1apm3dEsCAJ+hQOnSoeyMEbiUapJOtbzl+deL1nelyzwZH+CS52Va+BeHQyXjbmjGV7cvgenUbpNNPU8S9lZ7X69bL3x2Nxq48HPnowvlsFu0qKpIBM0W+TzeVkTMZPJoFarcTgc2Gy2GWsvZjIZgsEgoVAIQRCwWq24XC4MBgO5XA6fzyd/F23d52PZM06yRa2HjZfMfuKRIfjLu2D0VVCoJEeW835SkrkIh8OyG83BDFEUCYfD+Hw+stksNTU1tLS0VK8Oe/sdY0SxiDdug4v+b14SUW9mrJDFFSw6VCqVnAYsNsPs27dvyTTDGAceKR/cdU9lsvjwd8eIIsDOu+DZX8Px/7Fg8wMpEtrS0sLevXsZHh6mvb19QY/Z1i4Hj33hVEbCKeotOnTqcQTmpRsleZ+i08zac+HyP8+IML4+FOFbd26XX786FOGrt+/g1+9YT0NDg5yqLeopjpfDcblcxGIxdu/ejSiKsltGIBDA6/Wi1+tlWaTJjs1Ekmi323E6nTMiiaIo8vXbt/HnZwcQRGixGfjl5ZtwarJyqnk80XM6neyJwGfueAFhf4XDv7d7+M+zWzm8TjmjjuZipHJ0dJRCoYDuxG9gefw7KAoZyWLvrO9SMDaQF14tWzeTLy8lKGKTy1by+njl65yl38mx4kmIHZeAWo8qcwb03la6Ytsx0x4nhUJR+mAxB4xvVolGo3KZS2Nj44zr2YqdtYFAgFgshkqlwuFwUFtbi1qtJh6PMzAwIEd0i7aJ+nW/gkc6YNe9YGmSHENqO2f/Ie79okQUQRLXf/EP0H48HPo2eX7FurGFaPhZChAEQSaJRVH51tbW6rtpVSKEar1E0lcwJ6yQxRUcMBR9bK1WK4lEQq4p83g8B7YZxtJcPmYtrw3M5/Mo+p6kbIYDTy84WQSp5q2lpYX+/n6CweCCd3KrlApaayc8+eez47yr92PXPVKUsfu0abf52B5f2dg2b4a+pBYxlsVlV1eUwxFFkX379skET6PREAqFyGazmEymaeud5kMSi3hop5c/PTMgvx4Op/jSra/y43OaUCqVCIKATqfD4XDIhPU7D74kE8Ui/vF6gPPec9ikUcQi0uk0IyMjcv1mU1MT2o0b4eh3gvs1qN8A5gbMwFs2NXH3OHtBi17NOYc0Trrtza02PnxSF797vJdPKv/BNZq/gwDcexu88Vd4/91w+Dth8CnJ6QUR6tbBOf814+M1F2QyGblZpRhxbWpqwmq1zlhWpkhQAoGArNBQTFUX3ytaKOp0usoR3TO+Kf2bD/qfqjD2pEwW0+k02Wz2oBTiFgRBziblcjksFgttbW0LZ7m68a0Ij/wXytjI2NiWD4F6xQ1nrlghiys44FAoFNTU1FBTU0M6nT7wzTAnXAO7/w37U6HorXD8pwHI5XKSZ2s0SiKRwGVswxbYVbp+Kgy/PQ1s7XDS56Fhw4JN1Ww2U1tbi9vtpqampqoWaDNCKgSpYPl4oGdGZLHdUZ52UirgPdc9h1IBlx5Wx/sOkZYxmUxYLBb5hmO1WtFqtXK60GKx4HK5pkxlVYMkFvFif6hsbKdPIrRWq7WiWLMwkSkCGp0kQj3VnD0eT0UrQ0CSy+k+tWSdH112KC6bgUd3+2h3GPnU6WvketDJ8JVz1/PeI5w0/fYqGK92M/A09DwEq8+Ei38Jp34V0mGJnC5ANLtQKMjNKslkUo7y2e129Hr9jCPo2WxWTjUXCgUsFgvNzc0YDAaZeBeboywWi5wGXbAIff16iRxOHNuPcDiMSqVauo5Sc8BEG0yr1SqXiSwo9BZGzr0B4+s3YldEUaw+Gw67fGH3eZBjhSyuYElBr9fjcrlKnGH8fj82m23Bm2Ge6Q3wxyf3kcoVePepd3CW8DigILvuQqKCkUhPD6mUVNheU1NDc3MzpvO/Bzdth+jw/g9ghYH9EYThF6Wb7NUvTal/N180NjYSj8cZGhqiq6trcVP45gao3wjeN8YNKqS6xRng7I2NbO2s5dm+McJZ5FOCCH97xccR9Y2cuqFFTr8Wtfmi0SiFQmFG50Y1SWIR6xvL68rW1BtZu3btpBHCdxzdyr3b3CVj79xSuSmq6Fvt8XgQRVEWGJ9JitKoVfPlc9fz5XPXT7tsPp8nmUySTCYp+PehKqTLF4qNRSmxtszKm3wmmKxZpdhsMtO0rCiKJJNJAoEA0WhU9rUvdr6Hw2HZ9WcxxLVLcNZ/It54CYp0WHrdulXuvi+moA90CU61MP73VvyN1tXVLdrDbDqdJlwwYDrz2yjepFqV1caKzuIKljQm2p8tVDPMSwMh3varpymMi/x8/awOTm7TkU6n5ehnsfu4hAzkMxIpRIS/vEeqRxqP834CR3+ganOthGQySW9vL3V1dbN2d5kvMoMvI/7tKvTRXjDY4YxvwZHvn/H6BUHkoZ1e+vxxvn/PzrL3VQo4tcvEZ05yYTZoicViwASNxMm2XSgQCAQIBAJVI4nF5gh/IMgPHvPy1IDUkWw1aPj9+4/iyPbJo4QA/37DzQ1P95MrCLxzSxsXH15OvJLJJCMjI2VWhvOFKIpks1mSySSJRIJkMkk2mwWksgaj0UjTXe9G431tbCWVDj79GpgnT2PPFblcjnA4TDgcJpPJoNFoZE3E2XxHRTOAQCBAOp1Gp9NRW1uLzWYjl8sRDAYJh8MIgiBH4w+Edl/IPUDsldtxrT4UZddJcmQ2kUjQ19dXnU7gA4iJv7f5qgnMFYODgySTSdasWXNQkO+FxIrO4goOCixWM8yfnx0oIYoAt7w4wlmr11FXV4fZbJ48uqHWwdq3SNZ1ShUUSsliMpPDIIoLetEyGo3U19fj9Xoxm82L6u7iU9QRP/dm1jSZUZqcs+4EVykVnLmhgULByZ+e6mMgnCl5vyDCAz0JtKphrj62vrJG4ngMPIPw8k2kcwLulnNIWbpkncS5Eq6JOnwqlYo6p4M/fnA1e/wpvNEMW7tqJxeyHoezNjZy1sbKxCuXy+HxeAiHw+j1+hk59fzz5WFue3kYk07FVcd3clTHGFkVBIFUKiVHDpPJJIX956dOp6Ompgaj0YjRaJQtBnnXTXDnp6H3EXCuhrO+V1WiOFEeSKFQYLFYaGpqmvIhsM+f4O8vDlIQ4NIjWljdYJaJYNGJp6amhvb2dkwmE7FYjIGBAfn7qq2tpba2dtGJy3ikRQ2pzrNQdq8FYCiU5Pqn9tHnDnF0s46NGxfvd1tN5PN5mSSKoliVh7K5IpvNEolEaGqqvp7nmxkrZHEFywKTNcO43W6cTmd5M0w2IUVEVDM7xSvF17X7u2lnDI1BSiu98Ht5qKB3sM94GLreXhoaGha0Hqmuro5YLMbQ0BDd3d0L2hwUTGT57eO97ByJ0G7K8+FT1qC0zl0bLhqNMjIywseOtvG9R33Es+Wdu88OZfj5mjVTfq7CzntR3vIulKKAEejc8Tfy778XTXOFpqUZYKIEzngdvuLDw8ZmLRtnufl8QeC5viAatZKj2qU0WbGLW6FQ0NzcjN1un/Zmd9Oz/Xz1tm3y6/u3e7jxvYfRYVWRTCZJpVKI+x9UjEYjtbW1Mjmc9Dja2uCKf1R+b4a449URfvd4L6lsgUuPdPGRk7rIZDKy5E2hUJCbVWw227Tn6hsjES679mnZOvD3T/Txs4s6aTPm5ZrGosRSKBRieHiYfD6P0WicdSp7IVFssAHJHvHiXzyFPy49HD2wB/L6Hj5x6qoDOcVZIZ/P4/f7CQaDiKJIbW0tTqfzgBouFO1A36xWiQuFFbK4gmWFSs0wHo9Hboap1ebQ3nW11I1rsMPJX4JjPjrtdt+5pZXbXh4q6VR999b22U/wLT8Cx2rYez/YO1Ad9x+0aevweDzs27cPk8lEY2PjgnQBjnd3cbvdtLRUt66siHxB4PLfPM1uT1weG8328+srZk4Wb39lmDteGcGsU3HeGhNNOkmLcFODnpve0cnvXo5x5zZvyToNVsOUYtqBQADTQz/CNK4zW1HIoHnx99B65IznVqyfK9a9AXLDSjW+t6FQknf/7ln6A1L6emOTme+eXo+GPLW1tdTX18+4hu7GccLbALmCyPVP7OVTxzdgNBppaGjAZDKVN4akI1DQTGnXN1c8ttvHf9z8svz6v+7dSSgY4ILVEkG12WzYbLZZHcvrHu8r8ZjOFgRufMHNz99+CDabjVQqhdvtLpe9WQKC/+ORTqdlEvPPl4dloljEbx/vXRZkMZfLySRRoVDIJHFRaj+nQPHhrq6ubkk8HBxMWCGLK1i2qNQMY3z882hHn5AWSIXgvi9C02HQfuyU2zqqo5YbrtrKH56UbkqXHenikiPmYKWnUkt6jOM0GWtATot5PB56enqwWCw0NDRUveB7vLuL2WxekFrfJ3sCJUQRJL3A0UiKJuv0BOAPT/bx7XHaivduU/Czc5vodEhSQDabjW+0ZXlh8AlGI1KzhUqp4NNnrC7b1sQaKWul5oxsbEafa2Ld20I1QPzk37tlogjwxmiM27br+MqFh82a3FSKiFusVtauXVs5KpmOwj8/BjvvlsoFjv4gnPXdqnY13/bycNnY/XuifPy0tVOXc0yBQCJbNpZFil719vaSzWanFTI/0CgUCuTzefk3n8oWypZJZQtyJHgpIpvN4vf7CYVCKBSK6UtCFhlFYf6FlhF7M2JpfMMrWME8oNFoZGcY5d+fKV9gz7+nJYsAJ6x2csJq5wLMELkuy2w2Ew6H8Xq97NmzB7vdTn19fVXTNgvt7pKrIO4sipCdQvR5PK5/al/J60xB5MlRkbOPXSMTiTqzjnv+40RufWmISCrHuZuaWN80RnyLJNHv9yOKImazmWw2S8B1Js2BN0q2z6HvmHI+EyVWinVvC9UA8cZItGxsOKWcUxTsXVvb+OYdY59XrVTwzq0dk8/7we9IwvEA+TQ8/X/QsBE2v2vW+54MRm05UbPVGCa1GpwJzju0iUd3l2pyHlWvxOPxyJJJM/GAPpBIp6UHmeL3fP5hzfz84b0lv5tLj3Qtyc+QzWbx+Xyyw0xdXR0Oh2NJkfLiNeGA6fMe5Fghiys4aKBSqcDaCqG+0jdsbQdmQhWgUCiw2+1YrVaCwaB8AXY4HFVL4xTdXfbs2bMg7i4nrHbSZNXLUT+ArZ21tDum7uIUBAG/308qUx4l0uh0ZREnu0nLB0/sKhmbSBItFgv5fJ5oNIrBYMByxueg3gEv/0kS4N36MVh3Xtn+io4gwWBQTl3a7XZqa2sXXN7jiHYbuzyl0c4j2uZWX/W+4zowaFXc9tIwJp2aD5zQyeZW2+Qr7H2gwtiDVSWLVxzbzq0vDZHOSSRIoYAPTfgep8JQKEkokWNjswXlfvvEy45oYcgX5uYXRigIIuettXLVSd049ruvLAcUyWKx6aPTaeL6K7fw84f24I6mOWtDY8Xo+YFEJpORr1FFL/Pa2tolScaKdZNO58I88L/ZsSKds4KDC2/8E/5+1Zh8TeMmuOpfoF2achSFQkH2NYYxr+Nq1NvEYjH6+/tpbm6eUvR5LugPJPjJ/bvZ5Y6xpbOWa85cg804eedjMplkeHiYTCbD3X15rn1yLFWpUSn45yeOZ2Pz5JGniSTRZrPJaeNiZHkqW7/x2yk2rBRTl0WJlTkd80wMAnvBuXbG9X++WIYPXP88rw1JgtAnranjV+85Ykad1POFeMPFKHofLh086fNw2tequp9d7hg3PdtPMlvgkiNaOK57+hu4IIh86R+v8bcXhxBFaKs1cu07D8WuyiwJ2Zv5YmRkhEQiwerVS4sQVkI6ncbn8xGJRFCr1TidzhlrfB4ICILA7t27MZvNC1arfbBipjxrhSyu4OCDf4/k42pugvUXgGZpFblXQj6fx+fzEQwGJVmWujpqa2vnfUMcHh4mHA6zatWqRRHEFUWRN0aiGLQquutqStxHDAYDLS0t6HQ6rn9qH3e8OoLVoOHDJ3VzbHflGqNKJLHY8VpMh83kJpZKpWStPZAcO4oNK3M+xi/fBPd+AbJx0Fnhop/DhosAifgMh1PUmXXoNZWjMDtGo2jVSrrrFsexQxAERp+/k8b7P4oqv79m0t4BH7gfauoXZQ5T4e7XRvnEn18qGTusUc9/nd0sR30PpOzNfNHb24tGo5mdwsIiI51O4/V6iUajaDQaWWliqZLEIoLBICMjI6xevXrxXayqidFX4eEfQLAXVp0Op34FdOXi/9XECllcwQqWIbLZLF6vl3A4jFarpb6+fl5akoIgsHfvXlQq1YK7u4xGUlz5h+fZ6ZZSrCetquVzx1hRK6GhoWFW5HciSSz6PwcCAQqFAg6Hg7q6uinTYYIgEI1GCQQCpFIp1Gq1rLU379Rl3Ac/3QCFcSl1rRk+u5OXPDk+9ZeXGQymsBo0fO289bztqAoEIZ8BhWrG8k7zgSAI9Pf3k0ql6KgzYdz3AGhrpIepBeiIngu+c+d2fv9kaQmJXq1k+3fOXvJkZTqIosjOnTtxOBzU1x94Yj4RqVQKr9dLLBZDo9FQV1c392j7IkMURXbv3o3BYKCtbemUHM0aCT/87xFjNrMA6y+Ed9y4oLtdEeVewQqWIbRaLS6XC6fTicfjYWhoCL/fL2s0RlN5/vWGG41awdkbG6dNXSqVSlwuF729vXi93gV1d/nhvTtlogjw2N4gm+q1fOqcTTOOCI1Pyxd12/R6PT6fj2w2i81mo76+fsrtZbNZOdVcKBQwmUy0trbOKE09NpEcDDwDeovUTT9ufqlUivyOh7EVJtReZmMI7m1cfXOS4bBkCxlJ5fjSP17n2G4HLvt+UpaJwZ2fkkomtCY49hNwypdmNq85QBRF2dGio6MDo8kEdQvrKDQXbGwuv1FtbLEuPGHpfQRe+bPUHX7UB6B5c9V3kc/nZW3JpYRkMonX6yUej6PVamU1guWU4o9EIuRyueVNFEFqPBtPFItj6YhkI3uAsUIWV7CCJQi9Xk97ezuJRAKPx0N/fz+etJJr7h4kksoD0Gzdxa0fP25auZrFcnd5eTBcNrYvpqhI7J7c6+dXj/YQSeW48LBm3ndMG8FgoIQkmkwmmTgWCd9k2nyiKJJIJAgGg7In8Jy19vx74ca3QmQAgFzbiXhP/x+SWYFMRtLF0+HAqlCiGKfpiErHoLKF4fBrJZsrCCJ3P7+bCzc1oNVqMT/2bbTbbpXezEThkR9A3VrY+NbZzXMGEEWRoaEh4vE4bW1tc7aSGwmneHiXl3qznlPX1qFWVZ/AXbi5mXteH+XBnZK+Zq1JyzfO31D1/ZRgx51wyxXA/gTbq7fAB/4FzYdXbRc9vjh/eaaXeDTKh+paWQpJskQigdfrJZFIoNPpcLlcy9KXWhRF/H4/NTU1C6Jdu6hQV7hOKTWgXBo0bWnMYgUrWEFFmEwmOjs7icfj/PefX5aJIsBIJM1vH+vjGxdMf0NdDHeXQ5qtJfqBAIe0lD8RbxuO8L7fP0d+vwL6a0MR+odHuXyTRO4sFguBQICBgQGZNJvNlet2CoUC4XCYYDBIJpNBp9PN2BWk0rZSqRSau76Abj9RBNAMPI7m9T9jPPwqnE4nBoMBnW4jiuRX4OHvAaKUTj7zO9Q1NFGj2048ky/ZdptV8rTO5XKY9/yrfOe7/111siiKIsPDw0QiEdra2iY9htPhoZ0ePnrjS2QLEjE+vM3GzR86ZtJazLlCo1Jy3fuP5vWhCP5EhmO7HFXfx3iIooj41C9QMq4Sq5CB534HF/+iKvt4sT/Iu377LJn98jh37n6GWz92HGsbF7YOrRKKD1Rer5dkMol+v0PVrCLuSwzxeJx0Ok1HR8eBnsr8sf4CCg/+J6ro0NjYke9fMs2ZK2RxBStY4lAoFJjNZgKZ8gv6vkBixttwuVzs3bt3wdxdvnDOWl4dCjMUklKwR3fYee+x5S44t740JBPFIh7oTfLVi48kGAzS19eHWq2eMiWWTqflhhVBEGbkLTweoiiSzWZLPJOLUcO1ntfKlq/PDcPEY3by52HTpeDeJkWibK0YgS+9ZR1fv32bLJh96REu3rJ1g7xf8ZkOSLpLt2WdgwB8oAe23y6lyg+5DAw2dntiPLzTS7PNwKG1ArFIWLa7myu+e/cOmSgCvDwQ5o5XR3h7pTrMKmCTq/opN1EUyWQypFIp0um0/H9HPERZnD2XrLSJOeHaR3ploggQz+T57eO9/Phth02xVnVRlInyer2kUim5ts9sNi9bkliEz+fDYDDMOWK+lFBQ6ek95Vc07vsH5pwPVp0Bh7/3QE9LxgpZXMEKFgLBPtj3BDjXQNvWqmzyhNXOMkHnE2chIl6Mui2Uu0u7w8TDnzuF5/uCGLQqDp9EO1BbIYWpUSnp7e0FpGYYh8NRVqsmiiLRaJRgMEgikUCtVuNwOKitrZ1WeLwYNRxPDgWhXERcpVKRrT8UTf+DpW+0TGIXWNsl/RuH9xzTzgmrnDzbF2BVvZkj28eOg0KhQHHa1+CmyyRRbABrG2z50JTzL0PPQ/Dnd4w12DzxP9y19UauvnNYJqnrnDquf99mbDbb7LY9Af2BJIcqeuhQeHha2IAPG/v8M3tIORAQBKEiMSz2cmq1WgwGA2azGdURV8CDXy3dwOZ3V20ugUSmfCxePrYQEEWRWCyG1+slnU5jMBgWVGx+sVH8Hbe1tR0Un8fr9ZLTO9Bf8N9wAL21J8MKWVzBCsYjMgRDL0j6jI7uuW3jxT/CXZ+BYj3boe+AS34z++1ERyQRZUszdJ3Gp05fzWAwyX3b3KiUCi470sUVx8zOv3q8u4vRaJx7V3AqDM/9FrzboeN4OOL9oFKjUSk5btXUBPbtR7dyw9P9JV6/564yYrfbqaurK5tTLpeTG1by+TxGo1GOllVqfpgYNUwkEmSz5ULgCoUCg8GA0WjEaDRiMBhQq9UoGv6fROYCe6UF154LR8zuCb/DaaLDOUm0o/NE+MRzsOMOSRZj4yVSdHA2ePj7pZ3YkQFGHvgloniRPLTTn+GZ4QwXzdyyuxyiyI2233Jc8iEAMqKaz+Q+zgmrq/MANF8IgiATwiIpLIpfg/SAZDBI7jEGgwG9Xl9anlD3SdBq4OUbpZqxYz4Gq8+o2vzeckgjLw+ES8c2NVVt+5VQfKjy+Xyk02mMRiMdHR0zjrovF/h8PnQ63ZzLK5YS0uk0gUCAhoaGqjtuVQsr0jlFCAJEh6GmQXJ+WMGbD8/+Bu770n5Bb4XUoTrbLtVcCn68tryr7QP3Q+uWmW9n133w1yvGCEHHifCef4BaSySVQ6VUUKObG9HL5/Ps2bMHo9E4t6dyoQC/ORncr4+N7SfEO91R/u+hvQyFUpy2rp6PntyNRqXAH89iN2pQq5SIosiLPW5+91gPkVSWM9Y6OH59K50NVnRq6UYuiiLJZJJt+9yMBiJ012qp3a+1N7GQvRg1TCQSJBIJUqkUlS5rOp0Ok8kkE0StVjv5ZxcEGHlJInN1a2d3fBYB4v9bjyI2UjL2l/wpfCn/4ZKxz5+9lk+cumruO+p9FG64sGQooXVg+uLuRZH8GY/i9zw+WlgsHVAoFDIx1Ov18v8HWvqlIIj85P5d/OW5QVRKBe87rmN+38cUEEWRSCSCz+cjk8lgMpmor68/KFK0E5FOp9m7dy8tLS3Y7XNzP1oqEEWR/v5+MpkMq1evXvRzdkU6ZzbY9wTc9jGp+9FUB+f+aEE6E1ewhJEMwv1fH3N+QYRHfwiHvRPss4jexdzlRBHAt2t2ZPFfXy6NHO17XKpPO/RtWA3ze/Is1gMODAwQCoVm7+7S+0gpUQTE1/+G+6jP8/bf9xJNS80drwyGeW0oTI8vQZ8/Qb1Zx1ffsppD7QL6dIIvnNLMjoiab969i/98YIhak5bvXbyRrS16fP4A339oiEf3SfVjnU4jf3h/J3q9nkwmIxPDZDJJLpcrm6JGo5EjhkajEV0FO8EpoVSC66jZHZdFQjqdJt14HLbY30vGh+pOhtGx1woFnLJ2PmFFwLezbMiUDUAquKBC3vl8viRamEql5O9ZoVCg1+sxmUw4nU70ev3sv985TywDj/0Y9vxLshY9+Qsl0koToVIq+PzZ6/j82esWbEqiKBIOh2V5qaKLyUKpHiwF+Hw+NBrNvEsslgJisZisVnCgH26mwgpZzGfhb1dCQpJrIOGDf3xEiuSYVjwm3zQI9IzVkBUhCuDdMTuyaGuXXDFC+8Y2o1BCxwnMOH4nFCQF/4nw7575PKaBxWLBbrfz9PZ+nvIOkhcUXHJEC1u7KjuplCBbXq+mEAX++eRrRNOl8g8P7PDKf3tjGT7392386R2drO9sQ6E1cOH1D8mdw8FEls/c8grXX+LiFZ8gE0WAPn+SL97yPN84pa4saqhSqdDr9bJ8hsFgqG639577Jc3FxkMkkVzlFNtOhWHbrdIx2nhxVX3Ji6RgZGQE3eFXY1ZmUO2+R4p+nvBp3nnIR3nhr6/wTG8QZ42Wz561dkoLxRmh/bjyMeeamRHFRAD2/IuHBvJ8f3cLqbyCtx3l4j9OWy17PouiSC6XK4kWplIp8nnpnFAqlZLnt8UiRwt1Ot2BS6fefY3kOw6S20bfY/DJ58HcuOhTEQRBJom5XA6LxTKlvNTBgmw2SyQSoampadmn1QVBwO12YzKZlnw6fYUserePEcUiChkYeFpyN1jBmwP16xF1ZhSZMVFpVFpoOWJ221Eq4dLr4NYPQGgfgs7C6MaPoc4ZmbEctlIlPazse7x0vOuU2c1lGoQxcc29o2QKEvn664uD/Po9R3LWxmlufKtOlyLwCZ88JLi2oGneBK/umXLVnAB+hQ2LxcIzvYEyiZl0XiSuc9AT8ZStu90jdVkXo0rFlPKC1vjc+0V49ldjr9edD5ffVHnZ6Cj87nSpnAWkusIr/lGZcE1EOgJ7HwSDDTpPkc6jcSgUCoyMjBCJRLBba2h+6cco9twrvbnqdNj6UVo0Bv7y4WNJZPLoNSpUyircSBs3wZnfkSzI8impGeetv5p+vYFn4E+XQjbOaYBT6OTy7Nf52QMpFIUc7zjMIRPDQkGK5qtUKgwGAzabTSb9Go1m6RCCfBZe+2vpWCYKb9wm1TouEgRBIBQK4fP5yOfzWCwW2tvbl5zg90LB7/ejUqmWffoZIBAIkM1ml0WTzgpZtLWBSicRxPFwLH2z9xVUD4LGiHvrN2h45juosjHJCu0tP5xbqs11FFz9MoT7UZob0UUSuN1uVCoVTufMotXRs36C97rLWVXoISHquFn3Ns61HUHz7GczKf707IBMFAFEEX73eN/0ZFFrgvfdCQ9+R3rYaj8B5Rnf4lKFlWsf6yeQGEufK4CJ1YPFxo9Opwm1UlEio6NUgCLuo05d3jF6iMvGhg0bFu+iGnNLTTzjsfMuGHm5smjzc78eI4ogkatHfiAdq6kw/KIkAp7eX77QchS87w5ZXy2VSjE4OEg+n8flcmHbfqPUkFHEtluhthtOk7p6TXOsZZ0Ux39K0nuLuaXr4kxSZfd/Q/LM3o9DlX28XfUIfyycwx2vjnB2u0QMHQ6HXGOoVquX9A1TBFCoyjMEqsVpSBAEgWAwiN/vJ5/PY7Vaqaure9OQRJDKE0KhEHV1dUs6ZTsT5HI5fD6f/BtY6lghi8ZaOPXL8MC35KHC4e9HVb9wNSYrWHoYHR0l3HA8tVe/hio+KMmhzMfAXamE2k4AnE4D+XxeJowzeSL+1WsCv0z8J40EiGAildGz54E9/PCyQ+c+pwlIZAplYxMjfZOifj288+aSITtw68eO49eP9TAUShFKZNk2QernrZubaDGKjI6OkkqluHyTlT+9Gpbfv+KoBjavbuPIDTpeC23j8T1+AOrMOr5+/sZFIxO5XI740C7sYvkxIjpakSyKkaFyIhEZKluuDPd/c4woAgy/AC/diLj1IwSDQdxuNzqdju7ubnQ6nSSbMxE9D8pkcUGgt05rOZbJF3h4p5dMXuAC324m3sq7FVJDToOthnXrDsD1VShIxy4VkjTsjDOv1c1kMgwPD2PpvBDnnlvG3jDVSd3sC4hCoSCTxEKhgM1mo66uTjoXFhu9j8Lj/0/yMd5wEZz42UVtdAoEAigUChyOGZTLLHF4PB4UCsWS9AqvhBWyCHDCZ2DNOQj9T9OfMaPrOr6qEZwVLG1EIhFCoRDNzc3ozbVgnmXDxwzQ0NBAoVBgeHgYlUo1bXd/kWS5GbsovjFaoXFmHnjr4S3c8WppR+0lR8xPrLvDaeIHlxxKnz/BqT9+pOz9M10wNDQkN6B8+sy1vO1Ygd3+NIe67CXOFjd+YCuvDYUJJXNs7axdUDcPkKIW0WiUSCRCIpFAgZ2amhY08XHRQq1Jkr6psG7IfiR1/K30jTXnTLtf0bujjGQK3u0MDgwQi8VwOBw0NDSMRVLsneUbqZ2jzFOV4ItleNuvnmLffgcfg34NZ/FsyTJPCoegUir4yCkL0w08JTJxuP4CqcMdQGuG99w6rQaqKIoyYVer1egv/DHs3CI57tha4birZ0U6Z4NCoUAgIFlgCoKA3W7H6XTO2Ge96vDukEoLhP0NZd43IBuDs767KLsvHg+73b4gDlSLiWQySTgcprm5edl8lhWyWET9epT16zF5vfh8Purr6+euQbeCZYNsNitFDPY3fCwUFAoFzc3NFAoFBgcHZd2zyXBkm53HdvtKxo6YROR6rjh1XT0/fcdhXPdEH+mcwNuOdPGBEyoQkYkYeUVKfeoscPh7wFKuGzeZ8LDOWse6dU0lvy2nEw7rqLyrQ1226eczDxQKBWKxGJFIhHg8jiiKmEwmmpubsVqtqLzvlLpf5RVyEB6EhjGLxaKNoqL5VCzHfBrdy7+XJJQOuQRO+9q0+0/XH45p3/0l425dtyw4XPZgcfynKOy4C1Vif12n0QEnfX5ex2G+uO6JPpkoAnw1/V46rXFWZ95AVGoIaJv5f+o/orA/glH9HeDkxZ3gy38aI4ogkZz7vyH5QE+CYjQxmUxSW1tLQ0ODdGM/+oPSvwVCPp+XSaIoirL+6AHX33vtr2NEsYiXb1o0shgMBhFFccalPEsVoihlVvR6/bKqu1xhQxNQW1uLz+eT6yJWcPBCEAQGBwdRqVS0tLQseIqzaLnX399Pf38/nZ2dk3YufvDETp7fF+SJvVIadnOrjU+dXv062rce7uKth8/Cam7nPXDLu8cEx5+9Fj78qBRlGYfDWm00WfWMRsY6zOvNOk5c34JafWBrjQRBIB6PE4lEiEajiKKIwWCgsbERi8VSelPecVfpyoUsvHQ9vOWHcidjMBiU5UrU674NZ31DSnlOo9eaSqUYGBhAuelqulJeVJ5XERUqgp0XkF51Ht2tbRWjSKKtjd5zb6HW8yQOmxXWnw+GA3vT6fHFS177sPMJ/Q/49ydWo7jtYzj7Htn/xivw57fD1S+BtfqWk1DaYV38Z9n7HLaJC/p3Tbp+IBDA4/Gg0Wjo7OxcFK3CfD6P3++XSVFtbS1Op/PAk8Qi1BXq6jSL03ktCAKBQACbzbZ0jsccEQ6HSaVSdHZ2Luka3YlYIYsToFarsVqtBAIBnE7nsvoyVzA7eDwe0uk0nZ2d80sFFPLw4h8kvc66dbD1I5OmppRKJW1tbfT19dHf309XV1dFQmDSqfnTB7ey1xsnLwisa1xgUfqZ4vEfjxFFgGQAXrgOzvhWyWIalZI/XHk037z9DV4ZDHOYy8Y3L9yA9gARRVEUSSQShMNhotEogiCg1+upr6/HarVOmtoT8tmy2juEPOl0msHBQbLZLE1NTdTW1o5dK5SqKeV1xqc29Xo9rZuORTzsIYa2P00sB7WuNXTW10967UkkEmREDfqtV8ISEVw+rtvB/ds9E8acoDUh9j1ammbPp2HXPbO3OKyAooPLxH9FK0elUoler0doPx723lq6ckd5OUEmk2FoaIhUKlWe/l8g5HI5mSQqFAqZJC61zFZ6/aVonvw5qtw4xYhF6gIPh8Pk8/llH1UsFAp4PB4sFsuyE0tfWmfjEoHT6SQcDhOJRA4K0c8VlCMWixEIBGhsbJy/eO0dn4RXxzV77LgDPvL4pIXfKpWKjo4Oent76evro6ura9Kn5VX1NfObW5WQyWSIRqPYIm7KZprwVVqFdY0WbvnIsQs+t8kgiiKpVEr+LRcKBbRaLQ6HA6vVWtaBuM+f4N/b3dgMWs7d1Eg6HiHf+hYaQ78Y26ZSTaTzPIZ7etBqtXR3d8+qk3G8BE5tbS2NjY0kk0mGhoYQNU5au1qpqZn6Ow8Gg+h0uiUluvyeY9p5YyTKbS8PUxBETl1bx6dO68Ib9ONU61HkU6UrzDISWilamE6nS2wctVoter1eFurW6/Vj0judnRDfA8//Tkqluo6W1A7Gbd/v9+P1ehckmpjJF3imN4hZr5bLSbLZLH6/n1AohEKhwOl04nA4lhxJBOn33xfMYTr3BlpH7kZRbHA5ZGGbe0D6bnw+HxaL5cA09VQRPp+PQqFAY+Pi63LOFyt2f5Ogr68PQRDo6upaiS4eZMjlcuzdu3fudnfjEffC/1tbGm0DeNffYM1ZU66azWbp7e1FrVbPP7pZZYiiSDqdJhqNEo1GyWQyKBQKWnf+Fsvrfyhd+N23VtVPdz4ozjsSiRCJRMjlcnK2wGazodfrK37fD+/y8uEbXiC3X0qo1arlR2fV095UR8PgnShf/zuCzoy3++34LYdMHnWKe6UaR/drkmPPCddI2okgRyNzuRwtLS1YLBa8+2ukTSYTLpdr2hRbPp9n165dNDQ0LMkoSziZJZ5Mo8zGCYVCALT1/AnzS78cW6hunVS6oKlMsmcaLZz4b0YRwGRQkvQZJ5aeTqcZHh4mlUrhdDqpr6+vajRxrzfGe373HO6oVJKxpcPOD85pJZ2IolQqcTgcOByOJfX7H498Pk9vr2QS0NXVtehkNhwOMzQ0RHd397IWHM9kMuzduxen00lDw4xVdxccK3Z/84TT6aS/v59kMrnswsUrmByiKDI4OIhCoahOnWI+XU4UAXLlLicTodVq6ejokFPSHR0di6IdFknm+NOz/fT6Epy42slFm5tRKBSyH3ORIOZyOZRKJRaLhYaGBmpqalCu/SEYdVKx+37nkKVAFDOZjEwQM5kMKpUKq9WK1WrFaDRW/p59uwAF1K3hx//aJRNFgMFIlueCWo45shmaP0Jsw7sYGpJkcNpdrspuC4IA118Ivh3S64GnYfB5uOpeQqEQIyMjcjRSqVTS19dHMpmkvr6eurq6GZ2LRQJmUyTgxbvA0gLdp89M+3CBkUwmifr9RKNRVCoVdXV11NbW8jv/B3klZ+AExSuMKps49JhPcbZGP6NooU6nK3Hn0el08xPqNtbKJSLjo4larZaurq4Fidb+4J6dMlEEeG5fiFteVPKhk7qpra1dsiQRpEh4f3+/HDhZbKJY/I6K3/9yRrGjfrn2QqyQxUlQU1ODTqcjEAiskMWDCF6vl2QySWdnZ3UufLY2aD8B+p+QhwSDA+WqM2e0ul6vp729nb6+PgYHBxdcyT+TL3DZr55ij1dqSLj1pSFe6PPxsa11RKNRCoUCarUai8Ui19WUzEepk9J341J4BwrZbJZoNEo4HCadTsvEtrGxkZqamsmPY3gIfnvKWPrcsZpI6KtAad2iP1koaWKpqanB5XJNft70PzlGFIsYeArPtkfx4cBms9Hc3Ew8Hmd4eBiFQjGrdKcoioRCIepDL6C+9bNjnantJ8AVt03bULMQEEWRWCyG3+8nmUyi1Wppbm7GZrOhVCoZCCT54X07EcUjuY8jATDf0UurWQn5rBwtLFo2ms1mOVK4kH7P6XSaoaEh0un0gkQTx+ONCVqjAP68XiYNt744xN9fHEKnUXLl8Z2cvGaeZGLkZcm+tOOEedkQFh+sM5kMnZ2dB0SyJx6Pk06n6ejoWPR9VxOxWIxYLEZra+uyFRNfIYuToCj8OTIyQjabPXDaViuoGuLxuCyLVNUHgLffAA9+G/Y9QcrcwfDaK2lFw0yra4rp8P7+foaHhxe0M/uhHV6ZKBZxywvDXLZWT6PDLnvwLtXSi3w+L0cQk8kkCoUCs9lMXV0dZrO59EJcyMHgc5K0zHiR/T+/rbTOMrCHn1lu4rLUlSX7OqHLRk9PT1kTSzpXYI8nTpvDiNUgpY0LQy9SuP/bVLpKxGIxWtYditVqxePxEAgExrqnZ/HAkkgkyGazOF74SamESf8TUp3spstmvK35omg5V7QrK57DZrO55Nx5bTjMxEKnWKaAJyFwiKtOJoaL5d5SrH/z+XwLGk0cjyPb7dz9+mjpWIdUt/iX5wb40j9el8cf2+3jLx8+li2dc9RuvO1j8Oqfpb+VGsmacQ7nhSiKDA8Pk0gkaG9vP2BRPZ/Ph8FgWNYBG1EUcbvdGI3GRS+nqyZWyOIUsNls8sW9qalcS24Fywf5fJ6hoSFMJlP10wAmB1z4vwBoCwWEnh6GhoZmVe9qNptxuVwMDQ2hUqlobGxckJtnLF3u0JITwNXWgdO8NC2nCoWCLJYdj0tEt6amRq77q5jG82yHmy4bs99bfwFc9gdQaRB9u8pEsI8QtnHWhgYe2OGhRqfmfVuaaFFGgNImlod3evnMX18hnMyh1yj5wllrOL8xjOOW89Hmk0xEsu5wWjafLqed0+k0jY2NOByOWX+/Qb+Php5bUIb3lb/pn9qTu1ooagAGg0EKhQIWiwWXyzUp4drUYkWhoIQwmvVqtm7swqhd3NtPKpVieHiYdDpNXV3dolnGffncdezxxtjtkc7dczc18vajJKmpm58bKFlWEOEvzw/MjSzue3KMKIL0QHHfl6RGlFlaEnq9XsLhMC6Xa9qGq4VCMpmUtUaX6sPrTBAIBMhkMnR3dy/rz7FCFqeAUqmktraWQCBAfX39kq4tWcHkEEVR6jYVRVwu14L+YIuajX19ffj9/lkRU5vNRqFQYHR0dMFqW05dV49OrSSTH6uzPHG1UyaKezwxvnv3Dt4YibC51c7Xz19Pu2Pxn+oFQZDFsmOxGKIoYjQaaWpqwmq1Th+Ru+9LpT7NO+6E1/9Gcs3F6NTGUvkPQGlv5zfvPYp4KoNndIRUMiELMRcJRSZf4LN/e5VwUorqpXMC371nJycf+gj1E4iiiJLopvdTc87Xie8Xfler1XR1dc0pSpPP5zE++UOce26uvEDXKWVDsXSOm58boM+f4LhuJ+cf2iSd+7kUPPBt6ZjU1MPJX4S1UzvNZDIZ/H4/4XCYmtGnaI1uQ9+yCfXad0+ptdfuMPG5s9by0/t3kxdE9Bol33vrpsmJ4tALsPcBsLXDxrdO2gQzGwiCIEcTi7aJixkpc9mN/OvTJ/HGSBSLXkObY4xYV7oWacS8JHxva5udO8zEEgiQIugJH1hm7kkWCATw+Xw0NjYeUDWQ4vdVsT54mSCfz+P1erHb7cu+5nJRyOIvfvELfvSjH+F2uznssMP4+c9/zpYtWxZj1/NGbW2tLG+wFLsPVzA9/H4/8Xic9vb2RRF0NZlMOJ1OvF6vXIM1UzgcDvL5PB6PB5VKRW1tda3EfnDvjhKi2GDW8b+XSz7H2bzAFdeNdW0+sMNDry/OA9ecjFK5OCnC8WLZRS3EhoYGLBbLjEtBBEFAMfxSWfQwtutR+tWHYj/kIzS//OOx95VquOB/ZCcWgPb29rKb1D5/kmAiWzImiJBUlJNpUWuk5uIf43a7CYVCWK3W2Vt7jbwCqSC0H08oFKW27/by/ai0KE75MrSXShTlCgJv//Uz7BiV6uVufm6QVwfDfO38DRKRfvGP0oLRIUlk/SOPQcPG0m3vb3jy+/3EYjHUajUdvTdievFaaYHXgNdvgavum1JX8hOnruLSI1zs9cbZ1GLFapzkN/jsr+HeL4y9fuE6uPLeWUfFxuNARRMnQqFQcEhLubf2Fce088pgWH59jHIH3+m9GnYEQKWDU74EJ14zs520H18+VtsN5plnxSKRCKOjo3KH9oFCOp2WyjcWwSxhIeHxSNqjS6n7ea5YcLJ4yy23cM011/CrX/2KrVu38rOf/Yyzzz6bXbt2LQsDbY1GI4t0zyV1tIIDi2Qyicfjwel0LuoTan19vUw+urq6ZnWDqq+vl/X4il291cBQKMltLw+XjHliGfqDSewmLc/1BUu6NgF6/QleH45wWKutKnOYiCIhKYplFwoFdDodTqcTq9U6Y121oqZiKBQiEonQZltLjfeFkmUiNatQq9XYz/wsiqPOg2d+AXobwklfxB3LE+zvn7KJpbXWQI1OTTxTmsr3159Aofd3qLJj0UrhyKvo6+0lm83S3NyM3W6f+bUjn4G/vBv2ShaAYk0jiRP+Hw5F+TmkOOnzFcnEQzu9MlEs4oan93HJWj3rXv1rqdC4kIdt/5DJoiiKRKNR/H4/qVQKnU5HS0sLVr0S5d8nyCYNPQc9D8HqqRu6Gq16Gq1TPDQVcvDw9yds+3nYeTdsvHjKbVfC+GiiXq9fsrIrlx7pwqBV8fcXhzCo4Ucjn0OXDEhvFjJSLfSac0rsJSdF/XrEs76L+OB3URbSYHHBJb+BGZ53iUSCoaEhrFbrgpXBzBQ+nw+NRrOsdY6L16OmpqYlqZ05Wyz4J/jJT37Chz70Ia68Uioe/9WvfsXdd9/N73//e770pS8t9O6rAofDId/MqnXjXsHCo+jDbDAYFv3JTqlU4nK56O3txev1zkqEVaFQ0NTURKFQkGsYq1E3FEnlqBUjnK56iYho4iHhCHKoCSWlaFmxWWMikpEASYd2rC6tkId9jwEK6DxpyqhSJRS1EIti2fl8Ho1Gg91ul8WyZ3qjyuVyhMNhwuEwmUwGjUaDw+FAd9FPEf5yOcqYRI4jLaei2nw5a5v3lyEYj4BLr5vaiWUCjFo137xgA1+57XVyBREFcOlGC67WRnr0v6ap76+YClFS7aexz3EqWpi1aDcgCbzvHfOKVsTdOF/6Kfkj3o/22f+TxwWtGeXh76m4iUgqVzaWLYikcgUEbQ3KifWVeiuFQoFwOIzf7yeXy2EymWhvb5c7y4XwoCQVNRFx7+w+3wTk83livmHs6XD5m9GRWW8vmUwyPDxMNpudlSzRgcK5m5o4d1MTRIbgpxU+78DTMyOLQPrwD9Jn2EJ7rRZT66Ez/m2m02n6+/sxGo0HPJqXzWaJRCI0NTUt6e9tKhT9n3U6XdWzQwcKC0oWs9ksL774Il/+8pflMaVSyRlnnMHTTz9dtnwmkyGTycivo9FyyYEDgWI3lt/vXyGLM0E2KdUdqfXQfdqkTiYLiWI3X6FQOGAenAaDgfr6etneaTZdl0UdyEKhwMDAAJ2dnfiSIgVRpNM5txrCDbntPK7/DEakG/4OoZWPar7LsV1SummTy8qJq508vscvr3P6Gju1GkmU12Aw4NBmsf7zPSgCe6UFnGvh/XdJtW/78UxvgKFQihNWOUuiSePFsrPZ7My0ECug6O0cCoWIxWIoFAosFgtNTU2YTKb9cjd5Qmf+GWPwDZQmJw2HnIR1XGRpvOXebJxYLjvSxeZGHY9uG6DdpqHDYSSTydCweguGLWczPDpKJBLBbrfT1NQ0t5Tn6KtlQ4bwbpRn/5uspZnsq/8gZ3BiOP1L6CepRTt9XT0mrYpEtiCPHdNVy5EbVkPs83Dv58eORU0DvuYzCOzeTaFQwGq14nQ65UicKIqEw2E8niSt9g0YQ9vHdqQ2TBtVrIR8Pi83LSUSkiapoeFI9J4XxxZSqGDN2TPepiAIeL1e/H6/HE2cNVE/kKhpAFM9JCaQ78ZDZ7yJRCKBqK3B0Lp+xtqb2WyWffv2odVqaWtrO+DSLn6/H5VKhd1+YP3O54OiWkNHR8eyJbwTsaB3cb/fT6FQKIvqNDQ0sHPnzrLlf/CDH/Dtb397Iac0ZzgcDgYGBkgmk0vKZmvJwbcbrj8f4vt9YuvWw5X3zK5QuwoIBoNEo1FaW1sPqOyR0+kkGo0yNDTEqlWrSi/EcZ8URcpEYeMlZdEDpVJJa2srO/b0csXvnuaFYcky7ZiuWn59xVGTRgIng+LB78hEEWC9cpBbjtyFXnOxPPbb9x7F314cYttQhMPbbFx6pAu1UkEsFpM6YB/+rzGiCODfBU/8FM75AYIg8uEbX+CBHdLNTqNS8JPLNnGMS08kEinRQmxubi7XcJwG6XSaUChEOBymUChgMBhobm7GarWiUqlkUjM6Oirp9ynVmNafQf0En+ViZ3w8Hpct92Zyg8zn8wwPD5OJxTh9rYN0Ok2hUKCjowOVSkVvby/5fB6XyzW/9JnraHjh9yVDhcbD2TYc4yc7j2AgtprTnDV8rXXzpJtw1Oi4/qot/PC+nfT6Ehy/ysnXz99/fm39MNg7yG+7jaSyhlHXeRRSYLfbcDgcJb+XeDyO2+0mnU5L0kSX3wgPfhV6HwHnajjruyUPClOhSBCj0ajc1W4ymWhubsZisaBuvQHuuBp6HgZrK5z5bXB0z2jbyy2aWBEqDZz3Y7j1Q1IKGuCoD0Dr0TPeRDwex2g0zpjwFUW3FQoF7e3tB7yJM5/PEwqFDlhtaTVQ1GY1m80HrJN8IbCkEulf/vKXueaasfqb4s1+KcBsNqPVagkEAitkcSo8/N0xoghSh94z18JpX120KaRSKdxuN7W1tQc8EqxQKHC5XOzduxe3201z8/5IUHQEfnPK2LF64qdw+c1lFoEqlYp/DxRkogjwTG+Q/3toD189b2apKRnjSd5+NOaHSl7rNSquOKa9bLmiSLdw/3DZe7glnbiHd3llogiQK4h85843+P0lLqwWC/X19ZILzCxuAsXUaDgcJpVKoVKpsNls2O32kqjR+EYGkJw/XC5XWZ3adE0slSCKolz4L4qibI1lMploaWkhFovhdrvlTtv5+tfmN1xC4qXbsA78G4BMjYuR477Npdc+RV6QNGiuC4XYl3yB694/OZE4qqOWv330uLLPkkgk8GvXEF/zCdRqNQ6Ho8xJJJVK4fF4iMfjGAyGUvHwd91Stq9sXkCrLv9eK8kelRDE8bVcVpckLl7IT56NyGfg6f+TyKpjFcJxn8Kb1eP3+zEYDMsvmjgRGy6SRNYHngLHKqhfP+NVBUEgmUxOq6Jw+yvDUo2kRsU5XTrWO9RT+tMvJgKBgKxxvFyxnP2fp8KCkkWn04lKpZI7gorweDwVD6ROp1uyRuHFE3h0dJSGhoYVke7J4K0g31BJ0mGBUKxT1Ol0S+bHWpzL6OgoZrNZIijP/66UVAt5eOy/K/pJvzgQLht7fl9o9hPpOgVe/+uEsVNntQll+zEw/HzpYOtWgDKxbwBfskBr52psppn/rouEJhQKEY1GEUURs9lcUfS5KE0RDAbl8Updr4IgyJqp0zqxjEM+n2dkZIRoNIrZbEYQBCKRiGxlNzIyQiwWm9wreg4Y9fiIHfNtDOd9l9Ge7ahaj+T3L0ZloljEgzu9+OMZnDXTH9si4fX7/aTTafR6PS0tLQgaAzqNWiaK2WwWj8dDJBJBq9XS2tqKxWKZNEr31F4/X799Gz2+BIe6rPzgkk2sa6gpiSCOlz2yWCzTk5KpylbuuBpe209W+x6j8MZdBM+5mYbmdpxO5/KLJlaCySHpgs4SqVQKQRCmFLC+5fkBvnjrmAj4AzvgpiuPWBL33UKhQCAQwG63H/AI51yRzWbx+/1S3fQSOKbVxIKSRa1Wy5FHHsmDDz7IxRdfDEgX7QcffJBPfvKTC7nrBUFRpDsYDC4ZIrLk0HEC+HeXjrWfsGi7Hx0dJZ/Py/67SwW1tbVEo1GGh4dZvXo1qrinfKFYhTFgXaOFJ/cGSsbWN82hs/ucH0DcDX2PSbIcWz4kadnNBid+DoZfHrM37DxZ8ocGjusujwYc0mKZMVHMZrNymjmXy6HT6aivr8dms5URjKL1ndvtli3jil27E6OJs2liGY9IJMLIiNRwUF9fTygUQhAE2tvbUSqV9Pb2IggCbW1tVXNmKGpLtrS0kFGriVlydDmcBMY7zozDXm98SrJYKBRkp5VcLkdNTQ0dHR0UlFo+89dXeXiXF41SyeVHu/jIFgfhUAiVSjWjDu5oOseHb3xR7g5/bSjCVb9/lt9e1IxSITkTNTY2zowgToPbXh7i3ud3cu3I3xhPIzQpL6sLu9HUHTWv7R8MSCQSKJXKKbu+//RMuQj4P171cuyaA286EQwGEUVxWUvUud1u2Rf9YMOCp6GvueYa3ve+93HUUUexZcsWfvazn5FIJOTu6OWEou5dMBikrq5u2T79LChO+zp593bUQ88gokBxyKVw9AcWZddFotHS0rLknuqK6eg9e/YwMjJC6/oL4eU/lS40STThY6d08+huH3v3R+7aHUauPm317CdhcsL77pS6VzUG0M2BcBpscOXdkmOIQllSU3aoy8aX3rKO/3lgD6lcge46E//vbZun3FwxUhcOh+WbndVqlUVsK5GVVCrFyMgIqVRKfiCoFE2caxPLxGii0WjE6/Wi1+txuVxEo1E8Hg9GoxGXy1W1LEOhUGB4eJiamhpsNpscITcYDFx1fCf3vO4uWV6tVLC+qTJJzeVystOKIAjYbFI9YpFIfPW213lop1QykC0I3PDMALXKJO86phOHwzGja9uzvcEyGSFPPEdUaWbrmuaqpTVvfm6AL//jdazEQScyUUBTs3IdBqR6xSk90ZcwBEEgEAhUfDBcLojH40SjUVpaWg5KbrDgZPEd73gHPp+Pb3zjG7jdbjZv3sx99923bEUqiyLd4XB4WddVLBiMtfjO+yPJkZ10r1k/LyP72SCTyTA6OirXsy1FaDQampubGRoawtJ6DNZzfghP/gwhFSHcdhaWk79c8QfprNHxr0+fxFM9fgqCyPGrnGhU84iazrAhYUo4K5PVj57czXuOaScQz9BWW7nDeaImYjF15nK5sFgsk0aEi2Llof3RL5CyF5WiiXNtYhkfTWxpaeHfrw9z7/Y+nFYjHzq5hZGRERKJBHV1dWWNM/OFx+NBEASsjnq2D4fIhiK0uZpRKBQc1VHLJ09bxbUP76Ugglal4IeXHlrW5JROp+XrU9GByuFwlN2Ax3e8F9ETV89K+7apgm6iSqlgTVtDVW/4Nz3bD0CEGu4VtnK+6pmxN031sO7c+e1AKMC+x6WHn/YTZtxFvJQgCAKpVGrajNe7t7aVeFGrlAou39K20NObFuFwmHw+v2yjikX/Z4PBsKy1IafCojS4fPKTn1yWaedK0Gq1skj3TNNZbzYkEgn0DasXjSgKgsDg4CBqtXrJe3hbrVai0SgjIyMYj/wAmmM+ipDP4969m2wkQaOhcrRPpVRw4urlkdqo0al5pifAt+54A4VCwbu3tnH6+oZJNRHtdvuU0bliyrlIptRqNfl8flJHjrk0sYyPJlosFmpra7nu4R389Mliw06Ce7YH+L8LXGzZ0Fn1Lsd4PE4wGOQ5v4qf3PI48Uweq07JTy+v47T9z6SfO2stHzmpix5fglX1NdTopMu33LSy36lIo9HQ2Ng4Ze1Xh9PEQLBUa7GzbnaR5kNarJy3qYm7Xx8FQEuOzx6uol4nTLPmzFEoFMhlxzQjP5f7CD1iExebd9O+5lA46fNzi5AXER2F6y+AwH5v7foN8N47oGZ5/NaKSCQSiKI47Xl5+ZY2WQRcr1Fx5fEdHNl+YB+uRVHE5/NhsViWXEZopggGg6TTabq6ug5aTrCkuqGXCxwOB729vcRisarVKh0sKBQKpNPpRRUidbvdZDIZurq6lnz4X6FQ0NzczN69exkZGaGtrU3uSPX7/TidzmWv9n//dg8fumHMPeWhnV7+69x2DqmlTBNxugtrMplkdHRUdhLJZDKo1Wra29vLoolzbWIZH010uVwIgkB/fz+3bguXziUn8KxfxWlVJoqCIEgRS1HD9//dIzeyRDICn/3bazz95Tr0Gum8Nus1bN7vplNM4QcCAblpxeVyYbVapz2unztrDS/3h4jtTyN3Ok2879jyLvjp8PN3Hs5Fm5upefanHDN0Hco3crDbCOf/FA67fFbbCiaypHMFmm0G2UVmdHSUs1eZ2OWT1ADS6Phf4e2c+M5jaW+rAsl59IdjRBHAux2e/Bmc/b35b3sREY/HUavVMyqJuGhzCxdtblmEWc0MkUiEXC5HW9uBj3DOBcUmO5vNdlArpSzvu9IBgtFoxGg04vf7V8jiBCSTUrRiqo68aiISiRAMBmlqalqSdl6VoFaraW5uZmBggHA4jN1ux+FwEAgE8Pv9y755qpg2HI9/bvNz5js2YbPZKhJ6QRBJ5wsYtdIlaXzKWavVotVqyWQyk0YT59LEks/nGd0vom02m2lsbMTn88nfSV7hLlsnkxcrbGl+8Hq95HI5PHlzWcdzKJljrzde4itcKBQIBoMEAgHy+bzctDIb3cpDXTYe/cKpPLDdg0Gr4swNDTIhnQ2USgVnqV6EgV+NDeaScPsnoPv0GUXoCoLIV/7xOn9/aYiCILKlw85XT2lAlU9hNpv55Fu66G738fcXhzBqVbz/uE6OqAZRBPBsKx9zv1adbc8XiQAkfFC3dlrLvkQisSzrFUVRxO/3U1NTs2yu3xPh9XoRRXHZltbNFCtkcY5wOBwMDg6SSqWW7Um+EEgkEjN+wp0vstksw8PDctpwSSETh5dvlKSEOk6EQy4tqYWyWCzYbDZGR0cxmUxotdqDJrooVuBTJqNp0hrf218Z5vv37MATzXBku51vnNWBNivVMtbU1BCPxyf1951rE0uxFEAURVwuF3q9noGBAbLZLC0tLdjtdi49Is7PHxrTplQq4OLDqxuRSSaT+P1+Ghoa0Inl1xGlAu58bYR2hxGdUiQQCBAKhWS9R6fTOWddwVqTlrcfXQUd2yd/Xj4m5GH4BVj7lmlX/+sLg9zywqD8+rl9IX75ZJ4fvW2z/DC+UNEw0XU0iqEJUlCuLfPfsCBAOgwG+4y9mcln4NH/hl33QjYO0WHpODpWw+U3SaSx0mr5POl0elnW0MfjcdLpNB0dHQd6KnNCOp0mGAzS0FDdOt2liOV7RzrAKMpB+P3+JSMcfiARTmb583MD7Oj3cGyHlXXrFvYJVxRFBgcHUalU1fcyFUWIDIKpTuoani0EAW64EIb3W5e9dL3k73r+T0oWa2pqIpFIMDQ0RGdn50ETXXz31jYe3V0q9fKurZVTTH3+BJ+55RWKAbUX+0N87h8Jfvu21eRyOeLx+KTRxKKjSiwWm3ETy8RoYnNzM8lkkt7eXtRqdQnZ/PQZa9CqlNzx6ghWg4aPntwtp4DnC0EQEUWB4eFh9Ho9TqeTOoWCj5zUxa8f6x1bToRfP9rLM3s8fO80Sbe2KKK9FG5OgiCQLYhUpKuTkJuJeLonUDa23Z9flKyNd/37qdnzBKbA/mhi50myFNScsfvfcPc10jXEsRou+gW0bZ1+vXs+L10rJiKwB+78FFx1X8XVinaJy9EtxOfzyXa6yw1F/+fig/7BjhWyOEcURbrdbjeNjY1L4sJ9oJDM5rnkl0/R65cuWnfuCOPP6/iP0+cg7zJDeDweUqlU9esUR1+Dv18lXaB1Vjjjm7OX/ul9eIwoFvHS9XDqVyXB3f0oEt19+/YRCARwOp0HRXTxrI2N/Pa9R3HTs/0ogHdvbef09ZVTNI/t9jEh88qeQJZhf4R6q7FiNBGkJpbhwX4s++5lTWYQbecx0PB2YHKyWIwmCoKAy+XCbDbLuqlWq5Xm5uaSc0mlVHD16au5uorncTKb52u3bePO10YwaJRcst7MFy88Qn7Y+fK561nfZOHTt7xSst6rIwni6m6OXt28JOpyi9aKIyMj1LRfSPvIM6ULrL8QartmtK1V9eUkZ3XDPJpWZohIJIIvlkN5+T8wEZS6oSfp8p8xUmH42/ukVDxI15G/vhc+s02y85sMQgFe/cvk7w88LT3EVngojsfjaLXaZXcPSiaTJJNJ2trall36HKRrUCKRWBJ+2ouB5Xk3WiKw2+2ye8TBXq8wFe593S0TxSJ++1gvHzule34SL5MgFovJqbuqFxTf+sGxgvdMBO7+rJRGrlsz822kKrirCHnIxkrIIkjRAIfDgcfjkf8+GKKLZ25o4MwN0/8mXPZyIlijVdLeXE9zY7kjyvgmlrZnvoZl6GHpjVevh93/greXR2YKhQKjo6OEw2E5miiKIvv27SOdTs9KqHu++OG9O/nHy5JlYq5Q4I8vhznukAhnbRw7Ds22ytHsGrNlSRDFog9zJiP5F2s2vRWhpQnlM7+EdBSOeC8cN3P1i/cd28E9r4+y0x0DwG7U8LmzZhaVnCvS6bRcwuJ0OkFRpe7ngafHiGIRcbdkidlyxBQrKhBVWhRFT+iJqFs/aTq7WK+43ODz+dDpdDNSK1hqEASB0dFRampqluX854IVsjgPqFQq7Ha7LNL9Zni6qIRwKlc2lsjmyRWEqpPFXC7H0NAQNTU11dfkio6Cf9eEQRH6Hp0dWVx9JuitkI6MjbUcCfaOios3NDQQj8cZGhqiu7v7oIguzhSnrK3n2C4HT/eOpSI/ffoqXM3lEkjpdJqhoSGp0UUZHiOKRWz/J/5927jPbcZm1HDmhgYyyYQcTWxpacFms8nHWqlU0tnZuagdjOO9s4u4f7uHszaOPRgc1W5ndX1NiX3iphZrSZPLYiCRySOIIma9FLHKZrO43W6i0SggyYi1tbVJafvmS+CQS+a0H6tRw11Xn8Bje3wkMgVOXVcvywItBAqFAgMDA2g0mqqXsAjWtvLYtlIj+V5PAlEUCYZCCN2XUrfjj+ULaGvgLT+suG42myWbzS67NG46nSYWi1W/hGiR4Pf7yeVydHR0LMv5zwUH951oEVCMBIXD4aXXZLFIOHtjAz+8byfZ/Ji+2unrG+TO1mpBFEWGhoZkN5Sq/0iNDjDUQipYOu6cBVEEiSi+5za4/xsI3h3EHIdheOvPmKzlR6lU4nK56Onpwev1HjTRxZkgm0nzrVMcPOJSEBV0nLO5nU2u0k7XSk0sLzx+L5Xilp/83QM8k5dSiV21en5wRh0NtRZaWlpQq9V4PB78fj9msxmXy1WdSF0uDS/+UWroaNoMR10F2soEtNGqZzicKhmbKG6tVCr40we38rMH9vDGSITNrTY+NVUqvJCHkZckh54Zpn6nQr4g8PXbt/H3F4cQRDh/UyPXnNhILDz2u2hoaJidF7MgwOjLoDFB/bqyt9UqJaetW/jsTPEaUrQErWakNpvNMhDX4eg4H/u+u8beOP5TkwrhF2WTwuEwusM/QcbUgsP/HPqGbhRtxwGC5OluqNz9XaxXXG5k0efzodFolqWAdS6XO2j9n6fCClmcJ7RaLRaLBb/fP62X6sEKl93I7993ND/+9y6GQklOWVvP18/bUPX9+Hw+EokEHR0dCxNxU2vhrO/CHZ8EUSK+Udep6FuOmZToTQrXkZItniAwsmsX9pyOqWifwWCgrq5OFqc92KOLRSFer9eLTqfjvaceWrE2cbImlr26jXSLtTQpxgjMkOjk+fwYWeoNpnnWp+Lqw9vJ5/P09fWRTCZnT3Smw9/eB7v3Nx+8/jfY8y/JVrECPn3Gaj7wxxfIFqTzq9mq5z0V9A0bLHp+cMmm6fft2Q5/frvUTAFw6Dvg4mtBOXcS9Men9nHzc2Pdybe/OopBSPKew2wYDAZcLtekN8k9nhj/esNNrUnHhZubpQhheBD+dOlY1H7VGfCOP82teWye8Pl8xGIx2traqnqjj8fjDA4OSt7Ml18Ho89JqWfXFmg9uuI62WyWgYEB0uk0Wq2WbC6H47gPYqj9wqz2q9frl9U1IpvNEolEaGpqWpb3S7fbjUKhmJXb0cGA5XOGLWE4HA76+vqIx+NvmvqFiThhtZMTVi+cVVMikcDr9VJXV7ew9TmHvxvaj4O+x8jbOhjNN6Le3608lzIDpVKJzWYjFApRX18/5Tbq6+tl95H29vaDNrpYTCen0+lJO51hfxPL8DCiKNLW1lbSHXv6IS4+9K8v8SXl9Ryq7OMVoZvvF95LgVKS5E0Jcsc5QGdnZ3WjML5dY0SxiL7HYORlaD68bPETV9fxr8+cxD2vj2LWq7nosBasxnk0Jtzz+TGiCPDaLbDmnDmnhIGyTnaAl0ZSfP6c9VPWdt63bZRP/PllCvs7ln73eC+3feJ4rA98q7S8Y+8D8Px1s6prrAZisRiFJ/6XdftuR61UwFFXwvGfnrm0TQWIoiRn5Ha7MZlMtLa2SsSt8yTp3xRzKZ6TSqUSURRnXRJRdO5ZbtE5v98vl3AtNySTSSKRSFkz3JsBK2SxCjAajRgMBjm9tYLqIp/PMzg4iNFoXJynudpOqO1EDbSlUvT29jIyMjLn+pra2loCgQCRSGTKC2Qxvd7T00MgEMCX1/PFm99gMPoaR3XY+eYFG2mtXb4OAcVoos/nk9PJlaKJE51YWlpayjo9W2uNfPaKt/Ld+9YzGExyyrp6OgSBnW94SpY7tF7Lvn37Sm/k1fxMmRgVz4hMvNIoILmlfOLUVdKLVBgE85wjgeLwC+X7H3phXmSx3WHk8T2lY2uaa6eVB/nxv3fLRBGg15/gV/96hc/0PV0emZ+oFrDAyGazxB7/Nc2vjdOEfOBbklXg0R+UXr/+d3jouxD3wLrz4Nwfg8E26TYFQZI+ikQiOJ1OGhoapr0+jI+oa7Vaud5wLudmJpMhn88vqxR0Pp8nFAotyxr/olSOXq9flkR3vlghi1VAUUanGC2Zq0juCsohiqIcXWptbZ172mLkZXBvg9YtM9Z/Ayk93NzczPDwMAaDYU56WjqdjpqaGoLB4LQXGb1eT0NDA/uGRvj07aOEUpId2wM7vAwEk/zr0ycty9TNTKOJ45tYGhsbcTgck37eU9fVc+q6sYeHQDxDIlvg8T1+DBoVl22ys8GSo66ujvr6+qoft3w+z0jBSb25HX1snGuNrQ3ajp16Zf8e+MeHpVrDmgY48z/hsHfMeN+CIBAMBjHa1mD0T3Acad488w9RAe86vJ57Xh0mmCoAUnfyp86Yvm7XHUmXjQVTAkLjodAzXNU5zgaCIDAwMEDTwP3lb277h0QWR1+VlBDYT3Zf/5skZ/O2P1TcZjGFnMlkaG1txWqdvvmoUCgwNDRELBaTieJMSWYlJBIJFArFsiKLgUBAvl8uN4TDYVKpFJ2dncvyGjxfrJDFKsFqteJ2u/H7/bhck3e+rWB2CAQCxGIx2tvb564jdu+X4Nlrx16f8e1ZCe/a7XbS6bT8VDmXi3NtbS0DAwMkk8lpU00Oh4O/Pj8gE8Uidnvi7PLEWNe4fCwmZxpNnNjE0tXVNWtnJEeNjhs/sJWRQAS/ewSNEllPsdqQ/aSFPNlLb0D//M9g6EVoPkw6v1TTXFr/ftWYrVzcA//8KLiOAkf3lKuJokgkEsHj8ZDL5Wg46RsY/vVxFIn9XdbrL4CNc4sq5vN5qXM8FuVP71rDa0ElKJScc0gjNuP0Vbunr6/n9ldGSsYu3rIKvf0HcMN2CO8n1I41cOT75zTH2aL4sJnJZNDbG2Gig6PeJv2/4y5koljEjsp1p+PrE2d6nqbTaQYGBsjlcqjVavL5fFlpxWwRj8cxGo3LJkJXKBQIBALY7fZll8ItFAq43W6sVuuyIufVxApZrBKKT0ter5fGxsZlVXC8VJFMJvF4PDgcjrnf8H27S4kiwMPfh8OvKNM8nAqNjY2kUikGBwfp7u6eNXE1m81oNBopGjQNWVQoFNyxqzyNqQCshuUjvDvTaOKsnVi23y59h5EhWHM2nP9T0Fvl+rGg243JYKC1tbXqtpOFQoGRkREioQDtb/wfNXvvQKFQwpHvg0+9MrN0csxT7j8sCtDz0JRkMZFI4Ha7SaUkz+SOjg50ukNgwzZJY7KmYWZOIRNQJKCjo6MAtLa2YrFY2DDL6Ml3LjyEbF7g39s92I0arj5tNcd2OwAHNB8xRhYDuyXv6Hf8adZznS2CwSCRSASXy0VW/xF0u+5BKWSlN1VaOO5q6e9K3coTxiatT5wGkUiE4eFh+ZxWqVR0dnbOq8GmWK9YdfmwBUQwGEQUxWU15yJ8Ph+CIBx09eOzwQqjqSJqa2vxer0EAoE3tUh3NVAoFBgcHJTTsnNGYE/5WCED4X2zIosKhYK2tjb27t3LwMDArBteFAqFfH5M9zARiGdkgeLxOLzNRpN1lh2kkWF45AdSms11NJzyZaipkgDxJJhpNBGmbmKpCM8b8LcrQZRSpGy7FdyvU/jYMwwPDxONRnE4HDQ2NlY9VVScqyAIdLnvxrjrb2NvPvsrsLXDsR+Xh256tp//fXAPwUSWtxzSxHcu2gDZFEFfiHaNGVVuwnds76y430wmg9vtJhaLYTAYSpt00lEpnb37PlCqpQat834y4xrIXC7HyMgIsVgMq9VKU1PTnB90rUYN177nSPIFAZVSIR//gncXqu23lS68407JN71+/Zz2NRMkEglGR0dxOBwYjUZ6Ru2YL7iZFu/DKEQRNr8LGg8BwNd0GpYaF7r40NgGTvmS/Odc6xPdbjeBQEBOO1dyCpoLUqmU7J2+HCAIAoFAAJvNtuycZjKZDIFAgLq6umU392pihSxWESsi3dVBMXVUKBTm3IUso3UrqHQSQSzC6ICGQ2a9KbVaTVtbG319fYyOjtLS0jKr9YuOP8UC78lg0qkxalUks4WS8Q+eOEsNPaEAN1w0Rpjdr0mNBR95dHbbmQVmGk2cSRNLRey4c4woFuHfjfvR64k3HjPv1F4lFFNQoVBobK5PP1a+4O77ZLL4bG+Ar962TX7rjldHSMSjfOZYByaTieyJX8Tw0NfG1u0+Tfo3Dvl8XnaI0mg0uFwurFZrKUl56Luw+17pbyEn6T02HlrRorI/kGCPJ87hbTZqTVpCoRButxulUlnxuGXzAr95rIeHdnppsRv5xKndk5ZACIJANpslk8mU/a/zvEzFMzfhAyaQxZhb+o41BthwkdSAMgfkcrmSpri+vj6USiWNm05BoT6jZFmv14s3koJ33E7d8P0QG4W158lR2vH1iS6Xa0bdx/l8Xi47KRLF6WpwZ4N4PC7J9MyyVONAIRwOk8/nl2VUcXR0FLVavSznXk2skMUqw+FwyKmPN2PHVDUQCoWIRqPVSSOanBQu+iXiXZ9FnQ2DuRneei2o55YCMhqNJQ0vsxFiV6vVWK1WgsHglDp/eo2Kj5zUzU8f2C2PHeqyzsg+rwQDT5dHVkdfkfyvmw6d3bYqYCScIhDPsqHZglLBjKOJs2liKVtXVUOl9jGj7yWcx7+76iK58XhcfnBpbm6WtVQL5mbKYkPWVvnP+7d7Jr7LM4NJVl2xVWqA67wa1pwq+YjXdkvp9P2kuhiF8fkkCZuGhgYcDkcZ6RZFEXHvQ+WOIb0Pl5HF/75vJ9c+2oMoglat5PMnNXFssxq73U5jY2PFSNc373iDm58bAOClgTCP7vJy79XHYtEqykhhLjfm4qRUKtHpdHJjl67xbIQXW1DGxjW5mJug9ZjSHQ69CDdcCNn9JRgPfFvSq6wg4j0Vig0tIKXUR0ZGyGQydHV1lUVNPR4PPp+P+vp66urroXVVyftzqU9MJpMMDAwgiiIqlQpBEKou2ZRIJDCZTMui0aKYabBYLMtOxDoWixGPx2ltbX3TB39WyGKVUfS69Pv92Gy2ZfFjXkooNpLY7fYZdRjOBBHXaYyedxtrmsxoHJ3TNx9MA7vdTiqVkhteZqONVltbSzgcnlaT81NnrObwNhuP7fbR4TRx6RGu2VsnKieJ1Knml0oRRZGv3LaNvzw/gCiCy6bn26c30mCQ6pEm05OcTxNLLpdjdHSUeM1RrFNqUAqlFpPW1VtRVvFGND7yaTQa6ezslB9cEokEntZLad9z/1gq2VBb0jTVYCmntI1WQ6lSQuMhchoUpOMTDofxer3kcjkcDgd1dXUlBKdYqxaNRolEIrToG7Ew4YHAUUp4dnti/PKRHvl1Ni/wP0+M8tbPHIfTXvk3ls0L3PriUMlYNJ3nhoe3ccE6CwqFAq1Wi06nw2q1yuRQq9WiUqnKr3tX3Ar3fgGGX5L0J8/5L0kEfzwe+f4YUQRIeOHa4ySruy0fqjjPSnC73aTTaTo7O4lEIkQiEVpbW0vONVEU8Xq9+Hw+GhoayiL9c6lPFEWRUCjEyMgIGo2GfD6P0WiktbW1qulLQRBkcfnlgEgkQi6Xo62t7UBPZVYo+j+bTKaqZyuWI1bI4gLA4XCwb9++ZWvwfqAgCAKDg4NotVqamsq9geeKSCSC0WJHU1+5JmwuaGxslDscZ9PwYjBIhCEQCEzbtHPSmjpOWjP3+kKh5Siyjg3oA9vHBjtPmned2L/e8MgRJ4ChcJr/edLDXz58zKTEedZNLPtRvAEXXRN0ljoGt36H1me+jlLc3y3efjzKTW+b12caj2QyydDQELlcrizyGQ6HGR4exti4ET75POy4HRRKSdfQNJamettRLm58pp+BYBIApQI+c+bk8jPxeFwmORaLZX/zik4+BkUx4Gg0Sj6fR6PRYLfb0Z79bcSbL0GRDksbsnfCMR8v2fYbIxEmIp4VCOeUTJVYq/Sc63Q6WLOmE41GM7sH4fr1k7rayAj1l4+JBbj3i7D2XLBOX/YRCoUIBoM0NzfL5QNOp7PkwXM6ojiX+sTxtn3FtPNC1c4mk0lEUVzy95bhcIoX+oIYc2FW19csm5R5EcFgkGw2S1tb20rQhxWyuCAwmUzo9Xr8fv+S/0EvJYyMjJDNZunu7q5ayD+Xy5FIJGZdXzgdlEolra2t9PT0MDg4SEdHx4zmXOyaHx4eJpvNVr1btwhRFBkaHiZxwk9Y5b0XjW+7JM1y7Cfmve2XB0JlYzt8aZkoRtM57nhlhEgqxzmHNFKvF2fXxLIf6XSakZERkskkFouFTCZDKpVC4TqZvkvuozW7C62tRfLOrcLFXBAEvF4vfr8fg8FAe3t7CWErEgybzUZzc7P0fR/z0Yrbshm13PUfJ/DPl4fxx7Ocs7GRDc3lnzudTuPxeMqaV8YTxEgkQj6fl8sYrFYrBoNh/w2sUerC3nmPVOe39lzQlEY1D2+1o1CAOE4Zxlmjpa128rSoVq3knVva+ONT++SxWpOWS4/uXLBzltVnVm5IEwuSTuo0ZDGVSjEyMoLdbsdkMtHT00NNTU1JBE4URdkfvLGxsawObS71ieNt+zQaDblcbsbrzgXxeBy1Wr2kU7o3PzfA1/65TRZpv2JLC//ZcWDnNBsU64Vra2tXdJP3Y4UsLgDGE4IVke6ZIRwOEw6HaWlpqerxikQiKBSKBUkjaDQaueHF7XbT3Nw8o/WKmpzBYHDBpBjcbjfRaJS27o1oDp9GIHqWWN9Ufiw3NEuRm2Aiy0W/eILBYAqAn9y/i6+dVMep6+pn3MQynrRptVoaGxvxer3y+xaLhebmdahUlT1354JUKsXQ0BDZbLbMO3p8pGk2vtIWvYb3HtsBSNG9b96+DUGUoo7rG0xys5NGo6G1tRWz2Sx3PhdTd2q1GovFgtVqxWg0Vt6vwS51QU+CDqeJr567nv/+1y6yeQGrQcOPLjsMrXrCw41/Lww9JzV/NR3K18/fQFutkYd2enHZDXzk5G5qTQtEFAHx1K8QH9pBzdDDpa40CiU0Tu2TXWwo0ev11NfXs2/fPtRqdYmQ/3REcS71iRNt+xQKBd3d3Qt6zV/q9YqJTJ7v3rW9xM3nxueGec9x3axtXB4OZx6P503p/zwVVsjiAsFqtco1T9WOah1syGQyjIyMYLVaq/40Hg6HMZvNCyYCazQaaWpqYmRkBIPBMKOmptn4Rc8Ffr+fQCBAU1PTgpDkC1RPc5T5u6izYe4qHMOvNVfwrQs2AFJEoUgUAQoC3LIjwfvPbp/Rza3YUJLP56mrq0OlUskdu6IoljSZVAPj7df0en3Zjb5IQlKp1IydOibipYEQl//6GbIFAYA/PzfA985o4LAmIw0NDZhMJqLRKB6Ph2w2i0qlkglitUjBB0/s4pIjXPQHEqxvsqDXTPg9PPV/8O+vIQtTH/NxVOf8gKtO6OSqE6pXvjEVommBwWO+S3fwEXQPf1MqM1Co4LSvgr190vVEUWRwcBBBEOSGllwuR3d3t/y7n0gUDWYb37lzO4/u9tJea+TKoxuwE5tVfaLf78fj8cjRRLPZjMvlWlDB6UKhQCqVWtLNk0OhFIkJSg4AuzyxZUEWU6kUoVBoXjJSByNWjsQCQalUUltbK9fFrJx0lVGsU1Sr1TQ3N1f1aTmdTpNOpxf86bDY8DIyMoJOp5tRw8tM/aJni2g0KtdpLYil1uBzqP7xQVyIoIAPqu/lfUe1oWk7D4DRSKpsFV88P+33ms/nGR0dJRKJYDKZaGtrkzuCFQoFKpWKtra2qtY9TSfzk8lk6O/vlyWcZtPINB6/f6JPJooABUHkzt0JTtnQQigUwuPxyASxubl5waJGtSZt5chgMoj40H+iGO9g8swv4cgroW56m79qoEjaTSYTEedlRGo2s8oYR9V0CFindsTyeDwkEgk6OjoIhULEYjHa2tpKSgiKeodNTU04HA4+ftOL3PO6ZOfS40vwTK+fv1+5iY4O17THfrxtX5Eo1tfXU1dXt+DRvkQiAbCky5u66kw4a3T442NyZSqlgqPaly7BLaLo/6zT6WaldPFmwAqDWUAUyWIwGFwJZ08Ct9sty1pU+4k8EomgVCoX/MKqUChoamqSG15WrVo17cPBbPyip8O24QjRVI6NDXqGBgexWCwL1ym57VYm2qJptt8G5/03AKevb+BPzwyUvH/G+snnUuwAdrulG3dLSwsmk0muAQPpxljNiE0xKuT1eieV+UkkEgwMDKBWq+nu7p5XnV48ky8biySzBINBLBYLTU1NmEymBZXmKBQK5HI5WeZm/P8qz+t05st9nfHvWjSymEgk8IQT5Ay11ET9uJpXoZpBiUYkEpGjhYIgyDI4xYh6JaIYS+e4b1up718yJ/KyT2BD19Rkb7xtX1EWp729fUEsJSshHo+j0WgWrm60CtColPzP5Zv51F9ewR/PUKNT89Xz1tNsW/oNLpFIhGQySUdHx5JN8x8orJDFBYRarcZms8m6em92naaJiEajBINBmpqaqt4pVyQhVqt1UY57Udh4vMPLdBeb2fhFV0I6V+BDN7zA43v8ANSZVPz3ue2sXz99dGTOKHrpjodhbOzUtfV87bz1/OLhvcTSec45pJGvnV+5+zqTyTA8PEwymcRms9HY2Egmk6GnpwdBkCJx1RQynrjPyWR+ivInRqORtra2eZHUbDbLad1mHtnlKxm/5MhW1q1bXbVzsyiKPRkhLBTG0oIKhUImHAaDAW330QhPOFCmAmMbVGnLdRAXEL96aBe/fsZDThjCoFbww0utXDgNV0yn0wwPD8vp+r6+PiwWi9zdXIkoAqiVSjQqJZm8ULI9vXrq73mibV+xZnkxiJs/nuGvLwzSN+zlrHVO1lZjo9vvkJyH8mnJzeboD1ZjqwAcv8rJ018+jV5fApfdgEm39KlGsXveYrEs6cjtgcLS/waXORwOB6FQaEWkewKy2SzDw8OYzeYFCfenUilyuVzVtBpngokNL9PJ/5jNZkIZ+J9/78BitXLR5mZc9pmTxr++MCgTRQBfosANr8U49ciFI8eZTe9E9cyvUWfGdUSfcE3JMh88sYsPnNBJQRBRV9CGLEaA/H4/Go2Gjo4OOco6MjICIDcnVEvIeLzGo0ajqSiSPGnH8yyRzWZlmZtUKsWRDgWfOamZO7aHQaHgXVvbueqETh7c4eGnD+zGHclw5oYGvnreemomuakKglBGAKcjgxqNBr1ej9lsRqvVotVq0Wg0qNXqcvJ92XXwz49J7iUGO7zlRwtuC1lEjzvEL592U+yHSOVFvnb7ds7c2IxBW5nAFQoFBgYG0Gg0NDQ00NfXh1arxeWSHpSK6cSijM74a4xBq+LdW9v5/ZN98liLzcA5h1Rmp+PrHYuyOPM5P2YLbyzNBT9/Ak9USuv+/fUQ/6Ou4cLDZtZQVxE9D8Nfrxh7Pfyi1C4/Cz3L6aBRKZdFjWIRfr+fQqHwpvZ/ngorZHGBodfrqampkX0xV0Lb+2VdhoZQKpXyxb3aCIfDqNXqqromzAQmk4mmpiZGR0cxGAxTNuzs8sT46O1D+4vB3fzy4b3c8pFjOaRlZgT39aFy/bxtI9E5znx6FAoFBkI5VG+5kY7AIyjTYdj4Vug4oWxZhUKBWlX+vSYSCVk2qFgnCDA0NEQ4HAaYcZPBTFF8MEkkEpNqPM604zkQz/B/D+9l23CEza02PnHqKmxGLblcTpa5SaVSKBQKzGYzTqcTs9nMxo1KPnXu2Hb2eGJ85MYXye9nSDc/N0Ayk+WaUzvY7YnRadOgU45FC/P50lR2MTJYNAEovtZqtZXJ4HToPhU+vQ3C/WBpKZPfWUg8tXMYobSygWg6T48vXvG3ULx+5PN5urq6ZL/uojXoVESxiK+dt561jTU8uttHW62Jq47vqBj9yufzDA4Okkgk5PrEybY5LyT8EmGrWwv2jpK3bnluUCaKIBWB/PzBPfMji6/cVD728p+qShaXE7LZLH6/H6fTuaRT/AcSK2RxEeBwOOjv7yeZTC46eVmK8Hg8JJPJBalTBOlmEolExsh5OgLP/Ao8r4NrC2z58ILeDGtra0mlUgwPD6PT6SZNsf/60d6SrsFEtsCvHu3h/951xIz2c3ibnb9NcNk4vNU253lPheINOpfL0bZ+C0rdibNaP5/P43a7CYfDcnpXr9eTy+Xo7++X6xOr2ShQLEUYHR1FpVLJEcxKc5tJx7Moilxx3XNsH5UI+fP7Qjy918f/XtBKMplEoVDI9ZXTdeDf87pbJopF3Pmam7tfH6VdHCGhsvKBk9bwlg111NTUlEQGZy2IPVOo1ODorv52p0A2m6VJl0NBaSVsjU5Nh7PytdLn8xGLxWhvbycUCsnNLVqtFlEUGRkZIRQKTUnqlEoF7zi6jXccPbmrSNG2TxAE+eFiPo1Ok+LVv8AdV0MhK8kEnfR5OPUr8tuBRLZslUpjs4Kqgkaj+s0r8eZ2u1GpVGUC7SsYwwpZXATU1NSg0+nw+/1verIYj8fx+/00NDRU/6I7bh+FQkGK6oki3HAxjLwkvbnjTuh/Ct71lwXZN0hRtebm5hKHl0pRMm+svKnAOy6CMB0uO9LFo7u9/OsNyYe402niq+fNz51lMni93rIu08nw1F4/P7h3J33+BCescvDZU9vIxwJl0jfJZFLuNi7WfFarViiXyzE8PEw8Hsdms9HU1FSRvGUyGfbt2ydHpowGA6TCJXWYRbw0EJaJYhHbRuP0BDMc1d2CxWKZ8cOPzViuN9nFEL9W/5Ru5ShZUcX1T16A/eTrlkW9FwCCAANPgShA+/GgnP5YBAIBWmx6rjlzNT97cC8FQUSrVvKtCzdWTMnHYjG8Xi/19fUUCgUCgQCNjY3U1NSUEMWWlpY5l/2Mt+1Tq9UIglD1aLeMTBzu+bxEFEE6do/+N2x6Ozgl28a3HNJYIo4OcO6m+aVK80e8D9Vrf0EhjItYb/3IvLa5XBGPx4lGo7hcrpW+gimwTK5CyxtFke6iof1SVt5fSORyOQYHB6mpqSkTxK0mIpEIWq1W0ssbeHqMKBax+14I9CxoFKVIfsY7vEyMBp21oZEn9wZKxzbOvItZq1by6yuOotcXJ5rOc2iLFaWy+hGnSCQiS0BNp9vojaW56vrnSeek5oH73vAw5Atz7dvW0tjYKItyBwIBRkdHAckCsa2trSr+ucWo8ujoKAqFYkrHmKIIs1qtlryfh56Guz4NwV5wrIYLfw7t0wuaSwR4drWxF29u4TeP9TIcHpMa+i/N7+hWSsdEqyjwIf5Jzytvp3vrebPa9gFBwg/XXwjeN6TXzjXw3jvAMnndbj6fl5v/rl7fwKVHtrLLE+Mwl62ixE8mk2FwcBCz2UxNTQ19fX3YbDYcDkdlohjzwLPXQrAPVp0Bm98N05CB8bZ9xbTzTC3/5oRQH2Qmlo6I4H5NJotbte3t1QAAdnxJREFUuxz86LJD+b+H9xJKZDnv0Ga+eu6Gme/jpRvhjdvA6IDjPonYeChDQj3iab+m3Xs/ykIGNr8HVp9Rvc81+Dw8+G3pt9R9Kpz5n2BcelI0xZIFo9G4qPXtyxErZHGRYLPZZJHumTp9HEwopjEVCsWC1SmCdLGPRqNjNWeVJEFg8vEqQqvV0trayr59+/B4PGWF01cc0447muZPz/SDCO/c2saVx89eALmrbuE698Z3nM6E4D+0wysTxSK2eTPobfVoNJqSmzEwL//cgiDyz5eHeaE/yJoGM5cd3kzI7yEajWK1WqcU1S3reM6n4JYrILO/DjSwB255D3zmDblk4Yg2GxuaLCXRxcPbbGxsnv1NxmrUcPsnj+fmZwdwR9Mc2WrmqLt2ly3nir4ELAOy+MRPx4gigH83PPYjOP8nk64SDAYB5C7lZpthUnkVQRBkKaPGxkb6+vrQ6/XytXR4eFh2gLLb7VLE7ndnQGS/jNP2f4J3B5zz/UnnM962T61WUygUZmVPOSc4ViMa7ChS4xrGFEpoObJksbcd1crbjmqd/faf+Ck88K2x1zvvIvT2O4hnDLRvOBGl0g2eNyA6BIW8VIowX8R9cOPFkI1Lr1/+E8Tc8J5b57/tKiMYDJLJZOju7l7pJ5gGK2RxkVAU6Q4EAjQ0NCyoyv9ShM/nk2uLFlKgPBaLIQjC2FNix4lgbRu7aQA0bYaGjQs2h/GoqamhsbERt9vNcFzg5dE0bbVGTltXj1ql5IvnrOOL56xblLnMFvl8nv7+frRaLS0tLdNfTHf/m3Oe+R7HaYe5V9jC/8u/nSwa9BolJp2KfD7Pvn37SKfTKBQKWltb53Uj/vI/XuOvL4zVbP7t2R5+fE7ztHWHxY5nu90+JgS/77kxolhE0i95Eu+PLioUCm78wBZ++UgPrw9F2Nxm4+OnzD067azRcfXpq+XXoYc6sCf3lSyja57a5m7JYPTV8jH3a5MuLggCgUAAu90+I7eU4eFhcrkcHR0dDA8PA9DW1oZCoZCJYokf8447S3/zAC9cB6d/XfLQnoBilBmQReA7OzsXPguk0ZM880fo7/00qlxcqiU841tTOtbMCs/9rvR1LknhheupO/VrmG+7AgaflcZf/TPsewIu/V35NmaLXfeMEcUi9j4AiQCYFsAoYI4o+j/b7faqS7cdjFghi4sIh8OB3+8nGAy+qQppE4kEXq+Xurq6BdevCofDGAyGsYu8SgPvu4PCA98mN/gSqvZj0Zz9nQWdw0Q4HA7+9uIw//3wy3IR/3HdDm78wFZUC5A2rgbGW6gVu0ynhHsb/OWd2IQ8NiV8RHk3erJ8M38lHzyhCzGXYXd/P4IgoNVq5YaEucITTfP3Cc09270ZQhonGyYhilN2PNsq3JwVSrCVRnMcNTq+fv4sUoCzgP3SnyLc/C6U+f2p6cbDYPvtMPwCbP3otE4mBxStW2Hf46Vjri2TLh4KhSgUCjOKVhedjlpbWwmFQqRSKTo7O1Gr1ZWJIkAuWb6hQhYKuRKyWMm2z2q10tzcvCgP9EIhTzCWQX/MV6jr2ACNh1aXUInltnsatQprumeMKBbx+t8lojrf80xf4QFQpQP10iq/8nq9iKK4cAYGBxlWqjkXEWq1GqvVSjAYRBTF6Vc4CFCUnjAajQvuYpPP5+WGhhLUdiJe8jv2nv1nUmf9CMyLe3EoCCK/fdZT0u35VE+AB3d4FnUes4Hb7SaRSMxcdHjbrSCUyrtcqn4SvVrJy/v8PP3abgRBwGazsWrVqnnLU8TSuTK5FYB4VigfRDo3+vr6iEajtLa2lnRci6KIO2ci2HVR6UpbP7a4BK37NJTXbIfLfg9HvBfcr8Ib/4Cnfg6/PU2KzCxRZI7+GIm6cV38rVvhpM9VXLZI0KxW67TnQTwel+0rC4WC7NlrMBhkuaWJRFEQBEZtR1FQT2igW39BCZEpFAoMDg6WEMXGxsYF93eWkU1S+O0ZtD78Ceoe/wr87f2SdFEVkTv03SWvBaUW0wkfRpGJVVhahIrjs8Tac8E5QTZ8y4dAt3SErtPptOystmLFOzOsHKVFhsPhIBwOy9IuBzOK6SNRFBe0TrGIaDSKKIoVU5vFyFjRGWQxkcgUCCZzZeMDwQrRjyWAUCgku17MtHs/rzaWXUwiooF0XuDJvjCDwQS3f/ToqgnTr6o3s77Jwo5x9YN2o4YTV5dHqso6nsd14RfP0XA4TOO5P4HoB2D0FWg5CjqOr8pcZwVjLWy8BO76TOl43AOv/w2O+ejiz2kaiKLISCBG9oxfsdomoFQA9ZN35UejUblxZCpks1kGBwcxmUzU1NSwb98+amtrsdvtDA0NydHG8SUHxXXSWTXGS2/G+tIvxhpcTvuqvNxE2z5RFCsKtS8khBevR+N+eWwgHYb7vwHvv6sq2y8UCvS1vR17RoF16CHSShPqUz6LsWkjOLsQjE6UyTFRfxo3Tfm9zRhqHVx1H+knryU19DrWw9+K8rC3z3+7VUKxqUWr1a74P88CK2RxkWEwGDCZTAQCAaxW60FdVBsIBGS5lcUQOg2Hw9TU1FTsqi0e5/FOF4sFq1HDYa02Xh0Mj5sPnLxm6ZUiJJNJRkZGsNvtM76QRiIRPJZj6dLZS5xdfpM/X/57IJLDl1VTTQ+j373vKL5713ae6wuyttHMV85dj1FbekmLx+Oy00dnZ2fJeSgIAoODg8RisbHolPNk6Dq5irOcA0QRMZei7MqQSxyI2UyLcDhMIpGgvb0dZWY/qd15t2QhZylt5hNFEZ/Ph8lkmrJOrPjdKJVKGhoa6O/vx2g00tjYOClRLNYdKpVKurq6MBg2wvpTyrYdiUQYGhqSSaJOp6O1tbUq3fgywgPwwh8kAnjIpRWF69MDL1MmHubdXpXdFx+C8oUC6uM/we7hi6mrq5NTrhlByeAJP8W14zfowz3QthXO+l5V9g2AsZbs1qsZbhrAvG4dyiV0n4tGo2Pn64pUzoyxQhYPAJxOJ/39/aRSqQXTGjzQSKVSeDweHA7HwnYT7kc2myWZTNLS0lLxfYVCgVKpPCCRRYD/ecdmPn3LK7wyGMZh0vLFc9axumFpWWHlcjkGBgYwGAw0NTVN+yAjCAKjo6OEQiEszjb48CPw0h/wjPTz5V3dPCSMpSWVCrAZqngzRrJou/Y9R076figUYnh4GJPJVObxXCgU5N9ge3s7ZnMVvotsUpIoiY7A2nOkSM0sUfSnNbaehX3fuAiTWi+55SwxFMXWrVYr5uA2uOEiKOzXCn3q5/DBByUJGEEApZJEIkE6naajo6NsW95omr88P0g4mWNLk5pWg9TQMjIyglKppLW1laGhIbmUoEgUx9cdTqWHON62r5h2djgcNDQ0VJc0hAfh1ydDSur25oXfw1t/A4e9Q14km80StKwvJ4vtx1VlCsFgkGg0SnNzs3xcimVARSIuONehvfKOaeWEDiYIgoDb7cZsNlfnN/8mwgpZPAAoOjL4/X7a2iZ3EFiuKNYC6XS6RSsejkQiKBSKKYmpSqU6YGSxw2nin584nkgyh0mnquiZfCBRlCYBqct0uptnKpVicHBQtj8rCm2Hj/4M/uFhQhEvjIyl2S/f0ka9ZXEcIsaTgpKO5/3I5XLs27ePfD5fPUeObBKuO0tyCQJ4+Htw8bWw+Z0z3kQsFmNkZIRCoYD+Lf+N+Fwdijf+Ib259jyoWXqetW63G0DyQf/LZ8aIIkhRtcf/n+SgtPteqGkkfehH0XeeV5bu9UbTnPfzJ/DFpPX/AHzv/NUU1F5GA3FO3LyG0dFRotFoiZxNoVBgeHiYaDRKXV0d9fX1FR9yxtv2qdVq8vl8eVNMtfDiH8eIYhFP/LSELHo8HhIdZ5NL7UX9+s0oxILU3HLOf81796lUCrfbjd1uJxKJlJUBeb1eMpkMXV1dCxpZG18TvFTg9/vJ5/Mr/s9zwApZPAAoinSPjo6SzWYPKi/KojhuPp+nu7t7wcP8T+71c+PT/URicS48xMHGKQrTD2RksQhrBeeOA43id5ZOp+nq6pqy4FsURQKBAB6PB51Ox6pVq9DpdHIdUNED/c8fWcPtr46y0x3jqA475x4yuThzNSEIghx9amxsxOFw4ItnuPd1NxqVkjPW1hLySNIrnZ2dknB7NbDt1jGiCIAID/3njMhiMZoYCoUwmUy0tLSgVQjQ86BEtECSNslE4fIKnr4HCLFYTNY2VKvVkpbeRPQ8KNVbAsRGcDz5TXTtR6BQrCpZ7ObnBmWiCJL133/d30s8W0AQofvJAF850cHRG7pkolisO8zn81PqISaTSQYHB2WnIKVSSUdHR/W++4lIR6YcS6VSRCIRmpubCTm+SajjnaxurUdZt2beuy4UCgwMDKDX61Gr1YRCITo6OuQU+3gHrTebXEw2m8Xn8+FwON60xhjzwQpZPECw2+14vV65keBgQSgUIhKJ4HK5FvwH+dReP1dc96zcFfv0QBx7rYNzJiEmS4EsLkUEAgG5q3SqG0gul2NoaIhEIoHT6aS+vh6lUlkStSkSNIVCweVbFjdqXtSFTKfTcppy23CEy3/zDPGM1Kn9Y4OK/72gjS2HzL8juwhBEMh49lJ25GKjIBRKbO9GX32Q4L9+gC7tZ4/jNNZe9Hmy8QiCIJREaNlxp1T3Nh4775YImbnKUZHhF+HeL0paia6j4dwfQ8PU8kBFcXWTyYQt+Arc9AVJiHsiEr6SlwpEaoYfhzWl3uKhZLnXcTQzVl/cE0hz/bYUpx8jEcJwOMzw8DBarZbu7u5JrzXBYLDEts9sNi9ot7MoigSaTsbB71CM1z/YdJn8vtvtRqfTYbfb6e3txeBsQ1k3/99KsU6xUCjQ0NDA0NBQiVxZPp9naGgIk8lUubko0COdB4PPSSUU53wfmg6b83yWWmTR4/Gs+D/PA0srF/YmglKpxG63y3pjBwPS6TSjo6PY7fZF6fS+6dmBMvmUG56eXHpihSyWY7w0yVTfWTQaZe/evWQyGTo6OmhsbESpVJJOp+np6ZHr0Eq0CxcRxXnkcjk6Ozvlerb/eXCPTBQBgqkC9w8WqkIU0+k0IyMj7Ny5k+GaTYgTW1JWn1VCFLPuHThuezsbk8+zSujjLb7rePGPn0ev17Nq1Spqa2vlY5fJTOIRXu0bby4FN70dhp6XdAj7n4Q/v0MiuVPA6/WSz+dprjWhuOU9JURRRAFGJ5z2dTCXP7gpik0vogh77oeHv8+7rK+jYOrf5osDETmCPTQ0hMVimZQoFjU1R0ZG0Gg05PN56uvry2pXq4mi6Lxb20n87J9BwyawuOD4T0nHAun3lkgkaGhooFAokEqlqlY7V6xTbGpqwu12l9QpFrMHkypTCALc9DbYe78kTt//BPzpUun8OAiQSCRkfdU3myFGtbASWTyAKIp0h0KhBfVKXgwUi6a1Wu2iRUoLFYT2Ko0VsUIWS1H02q2pqZm0trRYEB4MBjGbzWMpR8a6SnU6XVmn8WJifMdze3t7yTyGQuU3u+Hw3K0eBUEgEokQCoVIJpOoVCpqa2upXXUhCtP/wkPfhbgXVp8JF/xvybojj99AB6ValGflHsSt/6U852w2i8fjIaroZI2xEU1yXGp37Vum9Fqe0+fpe6JUPgUk55ORV8BVuXkolUrJqUzd8NNlbh0KRHjv7dB4CHljPaq7/kOOson161Fsepu04D2fg+clx5A1wKOrzufKyIcIxNK027S86i797tY0SH7QyWSSpqamEnI9HkX5nFQqJdcpV62JaRIUU+KFQoGOjg5qag6BY99fskwxqmg0GjGbzbLlZTXmlUwmcbvd1NbWytsdTwpDoZDcGFSx69v9GgR7SscSPsnVZfWZ85rbgY4sFh8wDAbDQS9Xt5BYIYsHEBqNBqvVSiAQkFN3yxXF+svFqFMs4vItrfxru7sk2PKurZOnc5RKJblcud7hmxHF2iaVSkVra2vFcy+dTjM4OEg2my1JkY5vILFarbS0tBwwCYpimrGmpobW1tayqMGpa+tKtBgBTlk7e3H4TCZDMBgkHA5TKBTkrluz2Tz22Y94Lxx+hSROrhq7IQuCQCwWI5nOl28XLUat5EPs8/kIBAKoVCqaWjtRf+jf8MRPwLdLsq084dOznnclFAoFYrEY0WiUrC/BqrIlFGCq/PBaTHXqdDrpATdbQX1AqYYa6eFjtOFU8mf+AdPwY+jrurAcfxVoTVLH8PPXlazWNnQXN158FWFtGy2t7Xzk5td4pldqFDHrVLx3Uw3ZbJaurq5Jm5Im2vZpNJoFl+6KxWIMDg6i0Wjo7u6edF+hUKjEhzgWi2EwGOYtCl1sKNTr9ahUKtlWtUgKM5mMnPGZzAYTYy0iitLU+f7xuWKp3M9CoZBcj71U5rQcsUIWDzCcTic9PT1Eo9HJf8hLHOFwmFAoRHNz88IVjVfAKWvr+e0VR3H90/soCCKXb2njwsOaJ11epVJNnt57E2G8125XV1cZwZrYxGJvbOWJwTgtsTCbXRYGBweJx+Ml9YkH4jNM1fFcxH+cvhp3JM0dr46gVil415Z23jXDWkpBEIhGowSDQTmKaLfbsdvtk9fjKhQyUcxkMoRCIbnUpOawtxLvvYkacUwv8QnHZZwkJNm9ux9RFKmrq8PpdO4noLVwwf/M+thUQj6flwliPB5HFEX0ej3WNcdT6D8X1e57xhbe/O5JvYkDgUDpjbflSHKrzkGz976xhY75ONTUyak/s+sIfLY1rF27ForEKOaGicQEyPr34dpyNBaziZs/dAzP9AbodwfoMmRw2momjYyNl89Rq9UIyRCuoTuxpIZQ+I/l/7d333FyluXi/z/Ty+7OzPbeU0khEFpCS6hBpQrI1wIoNgSPikcFj4p6jgc5YPmJitjAhoICggWkGhAC0gIkIT3b++70PvM8vz8mM7uTmU22zO7sLtf79doX7JPZmXsnm51r7vsqHPeRnI+bG/uYR8qFVBSFgYEB7HY7FosFRVHw+XzTPlFSVZWurq60PMWKiopUnmLyxMdgMBz2xEex1eFveTdF+8e0a2o9E2rHb011JHMhZzEej9Pf34/D4ViwbepmiwSLeWaxWLBarakm3fNNOBymp6cHu92es+kck3HWUZWcddTE2vPk9BhaVWH/M4npEC0boLQ1N/c7CwYHB1MtSA4N7pNJ8D6fj9LSUrY7NVz3vecJxxLP28mNBXz59IqDR235Gd+VreJ5vIDVbNDx3fet4X8vWYVGAyb9kfOVDg3yrFYrdXV12Gy2I+6gJncRR0ZG8Pv9qdzk4uJizGYzvrKneOsvtxPz9DNUeyaL15yXanNSUVGR08bQ0WgUj8eTakIMYLVaqaysxGazje6Ave83sOPP0PN6osBl+QVZ7y8SiTAwMEBJSQlWq5V+T4j9gz6sa27GUX4aJZEeilacAy2np47+zGYzgUCA4uLi9B20mjUohVVofaPH7DGjDevys1JVzYqiUGcMUmSPUlpaTlVVVda/57Htc/R6PfFYlKUvfgH9wMHq9Lcfho4tcPmvp/+kHpQs8HG5XIdt2ZM0NDSUCuggcWycLLiZjuTgg9ra2lSe4tgCjoGBAUKh0GFPfJIBp/fYL7Fo+SZMA28kClyOvmJaa5sLZP5z7kiwOAeUlZXR0dFBIBCYV+9+ku9a9Xr9uDs7c0nOgkVFgT+8P9E7DkCjhQt+CMd84PBfl0cj/ggxRcGsJl7wKyoqMlqNeL1eurq6AGhsbKSwsJD3/eafqUAR4Pl2P50xOyvyFCiOrXg+XLuUQ5kNhw8SDw3ydDodDocjFeQdSbYAs7a2FrvdnvYiXViznJYP/oC+vj4MwSBFBRYqKytztiMfiURSAWIgkOhzWVBQQHV1NTabLXswqtMnqnUPVuxmkyyQSE5U+cFTe/jBU3uIKSoWg4YvnHwCV553TGrnMHn0V1payvDwcMYOWjASo+ekW6jfejvGoe2E7ItwnfI1KmsSu77hcDg1ju/QSS1jJW8XiUTQarVoNBpadX2jgWLSjocT1eWO6VcdJ5vXh0KhCfVqjMViDA0NUVJSkgrQvV4ver1+Wn/v2fIUx6aUTLRNzsDAwME3j02YbKuBD015Tdnka2cxFAoxPDxMZWVlbqfzvENJsDgHFBUVYTAYGB4enlfBYn9/f6q563yoMMtZsLj/6dFAEUBVUJ/4KprVl4POwI4eD197eBtbO12sqrPzzQtWsqouP7vGkZjCF//0Bo+80YOiwol1Vr6xqYk2v47//v3rRGJxLl1bx8rixNFzYWEhdXV16PV6ApFY1vnV+4bzUyEZCoVob08c1ybGuU2/T1wkEknlIsZisXGDvGyOtIt4qHA4TF9fH16vF7PZnLPd2XA4jMfjwe12EwqF0Gg0FBYWUltbS1FR0bRz4oDU8XVDQwP7hwJ894nR6udgVOWOl0b44FmJ5yt59Gez2VLpNWPz+GKxGB0dHeirj0Zz4mZ279uDRmdIHW17PB66urrQ6/W0tLRkPJdOf4RbH9vJc3sGqLZquXptCU12PVarNTG9ZX9b9m8iOvXCpqRAIJBqXj/Rhu4DAwMAqR0/VVXxer0UFRVN+Q12sl2VxWJJy1NM/l0fsU3OQU6nk8HBQaqqqnI+aSufmwfJYiKDwUBpaWne1rGQSLA4B2g0GsrKyujt7aWqqmpevAvyeDwMDw9TVVU1b5q77h8O8dI+DwWVfhpLC478BeMZ3pdxSRMYpn3Xm+jsNVx9zzYGvIm+ca93uPjwPS/z/I0bJ3QEmmv3vHCAP2/tSX3+UleAH7/s5G9vvZ2qHP/H9n5uPK2cy05sTaswtRr1rKq181Z3epPhE5unnvQ+VYereJ6s5Iv1yMgIPp8PrVaLw+GgpKQkp7uISbFYjIGBAUZGRjAYDNTV1U1rLryqqoRCodQOYjgcRqPRUFRURFlZGUVFRTl98xaPx+np6cFms2Gz2Xh8T1fGbZzBGF3OAC3lhamjv4KCAjweT1qwoqpqYtScolBXV0d3dzf+iMqKZYk5vX19fQwNDWGz2aitrc36fVz/+9d4fu8wAN0u2DnUy0MfWUVTYy0ajQZfxXGYLOUYgmN6PNYeB9Nsep3s7Wg2m2loaJjQ7+lkYVRVVVUqkItEIkQikSlPEUnmHCuKQmlpaUae4hHb5Bzk8/no7u6muLh4RgOqfOwser3e1Jsbmf+cGxIszhEOh4P+/v5UADaXRSIRuru7KSoqmjfv2m75+9vc9ex+AL73wj/56nuO4sMnN0/tzlo2ABrGJuhHS5dBQRkv7e1LBYpJQ74wr7Y5Wb9o9tsjJV9Ux9q8eyijxdCT7VE++a7Mv8v/u3Q11/72VdqGAxj1Wq49vZXjmmY3WDxSxfNERSKRVJAXi8WwWCwztouY/JqhoSGGhhKtaSorKyktLT3iY7UP+/nyQ2/x4v4RFlcU8rX3HMW61lKCwWAqQEweu9psNiorKyksLJyxF8W+vj5UVU0VSKzOskteWmCkttiSOvqrqKhITaQZ+2ayr68Pv99Pc3MzT73Vwf8+vp8uT4wllUN8Zl0ZjYXqYfNQe5z+jJ9pX0Rhu1PD4iZNop1Tdx+2c39O3a5foBnYAQ3r4MyvTfn7H1tM5XA4qKmpmfBzndzdKikZ/Tfj9XpTu79TcaQ8RZfLdfg2OYwe3xcUFMxYClG+dhaT7b4KCgpk/nMOSbA4RyQrLUdGRigvL5+zx7rJZGiNRkNtbW1+8xT7toHRCiUth73Z/kFfKlAEUFS49bGdXHJM3dTG75Uvhfd8F578RmL+bcVRGN77CxorG6GwDB7tyfiSClt+xku1lheyeXf6FI0Ckw53ML2F0HjtKZdX23j68xvYP+SjvNA8q+MKx75Il5SUUF1dPemft+QuotPpxOv1pnYRi4uLJ7QjPtldxORjulwu+vv7icfjlJSUUF5ePuHj4E/85lV29nkB2Nnn5SP3vMyvLm2gQK+i0+mw2WxUV1dTUFAw47smPp8v1ekgGXgsqSziP85czA+f3oOigtWo41sXr8Ko09LelQiOzGYzAwMDNDU1pe7L6XSyeUc3Oqsds9PHFx7Ziz+SSAvZ3e/jK48Feeqz6ylxZD8ODQaDdHe2o9NA/NAOL0Ydw8PD9Pb2HmzntBzNmg3T/v7j8Xii+MPrpbKyclJN5/1+P16vl7q6urS/J6/XO+XgPpmnWFpamjVPMdkmx+FwjJvnmWwenmwrNNO/w2d7Z3F4eJhIJDIr39s7iQSLc0gyGdzlcs3ZHbuBgQECgQDNzc05yYWaEk8v3HsZ9B1MYl/2Hrj0l+O2xtjd78u4FooqdIwEWGWdYi7hcR9JtBgJjKQ1Sm4sLeC9x9bxwGujR3XnH13Door8vMP9xOktPPF2H50jiTzDskITnz1zMV968K20/pRXHH+4/pSaWV//RCueVVXluT1D7BnwcVJLCStqEn+f0Wg0FeRFo1HMZjM1NTXY7fYjvhGbyi5iUnIiTigUSu36ZW2zEwvDtgfBeQBaz4CGk4DErmIyUEwKxRTedqpcdkIiR262XgCTFb9WqzWj08F/bGxhrSOEWzWzYXUzNrMhLa9xeHgYs9lMQUEi3cPl9XHlPa/yVn8Y6Mes1xCKpQcRzlCc/a4YJY7MtYyMjNDb20tJgZnL1tbyh1e6U3+2uKKQoxyJ6uuysjIqKytz8hxFIhHa29uJRqOTbuqdzJmzWCxpQVs8Hsfv91NTM36Lr/Ek8xStVitarTYjTzH5Rl6v14/bJkdRlFTeb2Nj44xuSuQjUItGo6n5z7PZxu2dQILFOcRoNPLmMHzhH1sJo+P81TV8+oxF6HVzI+fC5/MxODhIRUVF6kUgL568eTRQBNj5V3jlbjjpk1lvfmyjA4NOQ3TMdkSx1cDiymkWF+hNWSdq3Hbpas5aXpEqcDlvnFnVs6HSZuaJz53OMzsHiCoqZy6roMCkp7jAxK9eaCMci3P5cfVcdlx93tZ4qLHVpkeqeL7u3tf4+1uj7Vc+f2YzFywpSB31JXMRD91F3Dvg4+ZHtvFau4sVNTZuPn8FS8rNE95FfHH/MP/ztx3s7vNxYksJXz1vMcZIIliyWq2HbRxNPAa/Oh86X0p8vvlWOOd/YP2ncViMGHVaIvH0QqwlDVWz/m9ucHCQaDSatkOjqiodIwHifhflBXpOXtKSmrucPPrT6/X4/f5UvlwsFuOXT+84GCgmHBooAmg1UO2w0D7s554X2hj2RTh3RSVrSlWcTifFxcVUV1fzrWYNaxpKeGHfMK3lBZzdZMTlTKTv5GoSVrK5t06ny1pkcyQej4dgMEhTU1Na0OTzJd64TvYIemyeYnFxMd3d3Wl5ipB4Ix8MBsctOEzeRygUmtWJS7O5s9jf349Go0mNORS5I8HiHPJ6h5OvPNaeOhL8/57aQ0xR+MK5y/K7MNKr6/I+iD35IjtGvH0LunGCxYoiM7e+dzU3P7IdbyhGWaGJ71x+9BHbqUyVVqvhvFXVnLcqf0HiWGaDLmMtZx9VydkT7E85myZT8fxq+0haoAjww3+2cXrtImqrq3E4HFlfNOOKykfueTlV6f1Ku5MP/XwLv7ioBotRf8RdRFcgwjX3vIw/kpif/NyeIT4+6OanlzRRX1+PzWY7/K7K7scyf4Y33wYnfBy71cRHTmnmJ5tHi6jWt5ayrmV2TxpCoRBDQ0OUlZWlnocdPR6uu/c1Dgz5Mes1fGxdLUcdlXgJGXv0Nzg4mJpOlSxoOTCS2Qz/0DdwV65rQquBC3/0PK5AIk3ikTd6+OjaYj515rK0vL8rTmjgsrW1dHZ2pgLTXI1ySx5nJ6f0TPYEJRk4FxUVZQSFyUr4yQZqQ0NDh81T9Pv9DA4OUllZOe6blIGBAdxuN/X19bPSdWO2dxYDgQAul4uampo5m8Y1n0mwOIc8vLUnI3fswde68xYsBiIxntjRT1xRWVoYRnuE6rpZU7UKnG1plwZ11UQ6OigtLc16VHfJsXWct7KaLmeAxtICjPq5sVsrRiUrno1G44RGtLUPZ7b1CcdVCstrKC0df+dme487oyWQKxSnN17Iu5Y1HTGX7Nk9Q6lAManNFUVfXIPdfvgdI1VVCQ3uJyMEDrsh7AO9iRvPW8ZJLSWpApfzjx5TgBDxw/Y/Q8gNy9+Tk76B2dbY3d2NwWBIC0huuH8rB4YSzb1DMZU7nuti0zFNLCm3po7+tFotbrc7lV/a29uL3+/n9BV1/GXXjrTHOXVRGVed3My2bjdr6h2cvKiMO57akwoUk/66J8BXLksvqkrm3UUikVRP0Fx83729vYyMjBw+R9bZlvg7MBbAyvdmjMQbGRlJHV0fev9erzct6J0Iv99Pf39/Kk9Ro9Gk5Skm8yqtVuu4O6vJFjmVlZWzPvxhNnYWxzaBz8dwiHcCCRbnEKsx891QtmuzoccV5NI7X6DHnehN5jBr+c3Vx86Ntj5nfh26XwdPIi9QrTsew8nX4vGGOHDgAGazmdLS0ozjQ4tRx+JKqY6bi6ZS8by+tSxjd6qx1Epz2eGPa4utRjQaOPQ1rKnqYKWyqsKBzdC/AxrXQ82atNuVF2bmIBp0Goqt4we38Xgcp9PJ8PAwmJaxRKNHo46ZFV1/IhSM7h5uWFqROcM6MAI/PwtGDu46Pvl1+MD9B6vzp88birJ/0E+pPkIwGKS5uTn178cViGTkUgJs2TeMXfHy2B4vD+/uxxOIsLG5gP+9Yhkul4vh4WGqq6s5qriE17p93PdyJ3FFZVlVEd+4cCX1JVZOXzIakAaj8YzHCEbTj+TD4TBtbW2oqkpzc3NOWncl8wEDgQA1NTXjB3Rtz8NvL4HYwZ6Nz30HPvY02BI5iMkZ39l2poPBIPF4fFK5j9nyFMfmiycD+3g8TnNzc9bg1ufz0dPTQ3Fxcc6O6SdiNjcVXC5X6mc275sZC5QEi3PI/zuhgd+82I43NPoi8vHTDl/pO1N+snlfKlAEcIUU7n6pl+82zYGjy7JF8B+vQ9uzYCxE03ASpUBJlYrP52NkZITu7u7UGLWxkxPE3DKdiucqu5nvvW8N3/zLDga8YZZWFvGdy48+4tfXl1i55Jj0IqQzl1WwsvbgjsuDH4e37h/9gjO/Bqd+PvXpSS0lrGspZcv+0RYuV69vorgg82cs2UomWblqs9korT8Fje0eePyriV2qlg1wwR1H/oZf+eVooAgQD8PT/5OTYPGPr3Ty9Ue244/EsRo03HhmAytXjgbdRWYDlTYT/Z704+R6u4GndvTygy1DqWsP7nBT9vhOLmwezRnVaDT878Wr+OxZi/EEo+MWTF2wpoafPbc/7Q3Ae4+tS/1/MBikra0NnU6Xs7y7ZOqDoig0NTUdPjd087dHA0UAby+8dBec/Q0gkeepqmrWnDmPx4NOp5twcJssWFFVlZKSklQ/xbHrG9smJ9tzkWyRY7Va8zZla6Z3Fsc2gc9rLv0CJ8HiHFJfYuUv15/Cr7e04wpGOP/oGjYeurswS5LHTWPty3Itb/RGWHRW2qVkY+KioqJUM9yRkZFUk9/xjqhFfkxmxvN43rO6hvNWVuMORinJEqyN57ZLV7NhaTmvdThZWWPngjUHd4Y6X0E3NlAE2Px/iep3S+J4S6PRcM9HjueRrT3sGfBxYnMJZy4ffROVPG4cHh7G7/ej1+spLy+nuLh4dGd++fmJD0WBibZQcXVkXnO2T/h7Hs+wL8x/PbQtVVQTiKrc+nQXF5+0lCJzYr06rYavvucoPvuHrcQO5sqcu6KSVmuYB7syJ6P85Y1u3rd8UUaAUlFkpqJo/GKRZVU2fnn18fzomb0M+yKct7KK689YDCTy/To7OzGZTDQ2NuZsMk1XVxdGo3Fiwae7O/OaJ3EtEokwPDxMeXl51hOYyU5tGRoawufzUVtbS29vL4WFhWlpAUdqkzPbLXIONVuPNzg4SDwen/P9iec7CRbnmKayAr52/lH5XgYnLyrjuT1DaddOWTQ32/lkYzKZqK6upqKiInUcNt4Rdb8nxO5+Lytr7Fl3h0RudDkDPPRaNypw/qpKFO/gpGc8Z6PTaiYUKCqKQjQaTX2cWK3n2DIH0WiUtv37iEajFLY/T0YWYCyUaNdkGc2FMul1GRXksVgMp9OZylmzWCzU1dVhs9nGz4OcTK+9xefAa79Ku9ReejKN49x8ot7qdmdUX/sjcXb2eTl+TAP296yuYW1jMc/vHaax1Moiu4bu7m5qSu2AJ+3rbSYd9fX1U+oleOrick5dnF5E53Q6U4MApnq/Y6mqytDQUGpHarxpMRmWngdbfph+bckmIFGJq9PpsrY9i0QihMPhCVfpJvMUy8rKcDqdaDSatHzxI7XJURSFjo4OFEWhubk5rwUfM7mzGA6HU7PH5fRoZkmwKLL6yMnN7O7z8vAbibFRm1ZWcf3Gxfle1qQlf3mXlJRkPaJ+YLuH7z21l5iiYtJr+fZ7V3HxMXVHvuPZ8taf4NnbITgCKy6Gs74BhvnXP2xHj4fL79qCL5xIsfjxM3u47bxazjp2SU5yzg4NBA/9iMVixOPp+XB6vR69Xo/BYKCgoACDwYDR8W7UV76FJj7muNVen2jEPo5Dj5rtdjulpaW5H4O5/D08aL+Ss11/xEqIp5Rj+cKed3Ffn4dlVVMPtpdUFqHTatKm+hj1WlrLM4tGqu0WLl1bRzweZ8+ePdhsNj5yahl/fqMP58HCFK0Grj9jcU5evMcGdcXFxTk5SlUUhe7ubtxuN+Xl5VRUVEz8Pjf+F96BdgoPPIrGUADrPgWrLiUYDOJ2u8etxPV6E/meEynEGZunCGTta3u4NjnJPMZkDl++gqjZ2Fns6+tL7dyLmSXBosjKqNfy3fet4ebzVxBX1Ukd8c1F2Y6o3+7o5ztPdqUq0MMxha/+eTtnH1VFoWkO/NPoeAke+CipsYIv/STx3/NuzduSpmL/oI+bHnwzFShCopr2sQMxzj/5yAHVoYFgLBbLCAYPDQR1Oh0GgyEtEBz7odfrx9mdKodLfwF//yJ4e6BsKVx8J2gzX5A9Hk+qcXfyBaukpGTGmtWHY3E+P7AJnXoWBmIESbxpeOrtgWkFizUOCzecvYTvPL4LRU3s1H75vGWH/Tc/9ujPaDTyt/84lV//aw99wy7ee1wjp66Y7n5nenXypIO6cUSjUdrb2wmHw9TX10+6MjikaGk/5kbq3v19HI4S0GpTDbhNJtO4lbher5eCgoIj7vBly1OsrKxMy8VLtsmpqKjI2gJntlvkHMlM7Sx6vV68Xm9OdprFkc2BV0Qxl83meLfZkjyifn1QQVG70v7MF45xYNDPqizzb2ebuv1BNBzyi3bbA/MqWLz/lU5ufODNrOMEB/0RFEXJGvxNNBC0Wq2p3cGxH9N68Vh+Pix9F9093fx5TwTDPg0XFYWosJkzjpqtVuvEeivmgFGnpbTAxJAPYmN+dVfZpr/TfN3GRVxwdA07ej2sqrVT4xg/iM929FdsgvObddjXtFBbWzvt9YzNZz1sdfIkBAIBOjoSeZ9H6uE5HqfTmRi5eDBQhES1sd/vHzcvUFEU/H4/lZVHLg4cHBzMyFMcW8E8tk1Ott20fLbIOZQ7GOWFjgCrDT5OylEPzKRkgG61WqeVwiImbsaCxW9961v87W9/Y+vWrRiNxtQRjRBzxdENJWg16XORi0x6WsrzW1GnKAputxslqJKR/WSZ/ovmbInGFb796M5x504fW65hx4703ntarTYV8FksFmw2W24DwQl6rcvD+3+2ndDBti0/emYvd126mCISYxNzdtQcj8KLd8Kex8HRCKd8LlHtn4VGo+E/z1nCTQ+NjmpcUWPj3atz0/y9vsRKfcmRd6IOPfqLxWJ0dHSkRipON2iOx+O0t7cTDAannc+a5HK56O7uxmw2T7k4RlEUnE4nJSUlqZ/BZNBSUFAwbkscn8+HqqpHbJnj9/sZGBg4bJ5iT0/PuG1ypt0iJx4DNT7u2NTJeHpnP5/63WuJfz/PDnLJMUMT6lRwJC/sG+Kvb/ZiIsapNRrWrV4qBYuzZMaCxUgkwmWXXca6dev4xS9+MVMPI8SU1TosfPldy7n1sZ1E4yoWg45vXbKKgjwdQUciEUZGRlLj5uzLLqV474NoA4MHb6FJa+Ey13mCUUb8kYzrJp2Gy9aUc/XJDZiMxrSj4bkyeeHHz+xNBYoA7mCM3/y7m5vfvTS3R82PfjHREgeA52D3o3D9KxmNnpOuOKGBFTV2ntrZT43Dwvmra2ZsElE2hx79JSe0KIqSk+PAaDRKW1sbsViM5ubmaR+jjm3N5HA4qKmpmfIa3W53atxektPpJBwOZx1WEI0r/GN7Hzva+ji6wsDKbDPCD0rmKSaPm7PlKbpcrtTx8qF5iOFwOJXnOOmAXVUTLZhe+kmimGvle+E930s0HZ8CRVH56p+3p/37efD1bi4+tjajcGkyHni1i8//8Y3R+zTreHTpUnKdGiyym7FXxW98I9F36p577pmphxBi2j56agsXHVPLnn4fK2pt2Myze+yuqqO9Ib1eL1qtNtUb0mQyQd1ziQrYwMECl8Z1s7q+6SgtNLG82sbbvaOVshoN/O0zp7GoYvoTN2ZSnyezHUxYa57azNlXfpkoVDLZYP310HQKAPGwH+3rvyXtZT0wDNsfguOvGffuVtXZ85Imke3or6+vL9UoerqFFMl+hwDNzc2Tnsd8qOSRrdfrnXJrprGcTicFBQWJf5ckdhoHBgaw2+0ZO8zRuMIVP32RV9udAGiAb+vsvO/4zIk7yYBbVVWKi4uz5ikerk1OLBajvb0dvV4/tRY5b/0Rnrt99PM37wNrGWz638ndz0HeUIxuVzDj+s5e77SCxTvHjMAEcIfi/OHfHdxwzvjFZyJ35lTOYjgcJhwerUL0eDyHubUQuVFWaKIsy1SOmZSc6DEyMkIkEkkd4TkcjvSdD1s1bLhxVteWSz+4Yg2f/v3r7Ozz4rAa+NKmZXM+UAQ456gqtnV7Mq5NhNMf4XcvtdPlDHK15q8se3M0x1Td+yQDF/weT0ETkYCH5apK5kv7zI9Hm4rh4WHC4TCtra1oNJq0CS3TbYbs9/vp6OhAr9fT1NQ07UlRyWbUybF7k5makk0oFCIQCFBfP9ouaWhoiHg8njUX8fHt/alAERJ/o7f9YxeXrq1Hp03/Gx8cHEzNt86Wp5gsetHpdBltcpItcuLxOK2trePuzKuqyt/f6uPlthGWVRVx8bG1mPSJ28bf/hsZX7XnH1MOFu1WA4srCtkz4Eu7vrZpemP4PMFo5rUxAyzEzJpTweItt9yS2pEUYiEa22ZFVVXsdju1tbULtln44soiHvvsaQx4Qzgsxnkzk/vaDa0M+8Lc/0oXBp2Gq09u5rLjjtxSyR+OcfGPn6ft4Nzqjxt/BWO+ZY0SxfT2H7GedjOlpaUoq96H9o3fjt7AUgJHXZzrb2fKonGFzbsG8QTD1Os81JQXY7FYCAaDdHd3pya0TIfH46GzsxOLxUJjY+OUUhF+9UIbP//XfoIRhQtWVXDJIj1Gg57W1tbUTuB0jIyMoNfrUzuq0Wg0NXUo245qz7ALG348jAbRQ74IwWg8rdOCz+dL5SmOjIxk5CnC+G1yJtMi57/+vI17Xxpt6v7w6118/6JWPB4PjngBGft99um1D7vtsqO59rev0usOYdBpuHbDIo5tmF6weOGaGn723IHU5xoNnH90bvJ1xZFNKli88cYbufXWw1divv322yxbtmxKi7npppu44YYbUp8nxxgJMZ8l26wMDw8TCASyT/RY4A43tWMuMui0fOPClXz9ghVHDOKj0SjBYJBgMMiDr/ekAkUAhczg2OEowZGsGD7/e1DWAnueSBS4nHpDaka0JxTFpNemdoBmmzsQ5X0/3ZKaCV1o1PK7j9ZQmcOCluRMcJvNRl1d3ZTyCR/b1sfNj2xPff7LLZ2o0XK+cvHanOTAKoqCy+VKjS2ERACn0WiypyU89x0+8sJ3+ZjZx7/iK/hc9DoGcXBCc0laoBiLxejq6jpsnuLh2uRMtEXOgCfEH/6dPv1nywEnz77dzbpFFZhP/wxq7zNovD2JPzRYYcNNk3qODrWm3sFzX9zIzj4v1XYzpTk4ufnCucvQajX89Y1e7BYDn9rYytrG+VPwN99NKlj8/Oc/z9VXX33Y27S0TH2Wsclkysm7QCFm27ZuN//aO0RzWQFnLa9Ep9UQjUZTBSuxWGxW26zMObEIvHEv9LwOtWvh6P8HurkfKB/69xSPxwkGg0S63kC78xHCWivDdWejGG3o9Xp8kfRJKL+On803tWOmruhMcOyVo5/rjYmipTGFS0O+MJ+7byvP7Rmi0KTnk6e3pEbezabfvNiWChQBfBGF7z65l69vLJ92QYuqqgwMDDA4OEhpaSlVVVVT/jfxt7d6M6493xnMWbFUsrAluYMaCoVwOp1UVVVlPsa+p+Gpb6aOdU/Rbeeb3M3ddf/Ndy8/OnWzZJ4iMG6e4uHa5EymRY4rGM3akaCorJq6uoM7c5/aAtsfhEgAjroQHNPfpNHrtKPz1nPAqNdy03nLuem85Tm7TzFxkwoWy8vLpVO6EIf45b8O8M2/jraAObm1mFvOrcPj8aDValNHddNN2J/X7v8Q7H4s8f+v3pPYSXvfb/K6pCNRFIVQKJTaNQwEAkQiEYp6nqNhy3+hURP9H8v33Ef8mifR26sprAzys38PEIklgsZfx8+lsbaGa2yvgNkOJ30KKg8/zvPmR7anRm36wjFuf3w3K2vtbJjlOfF7D8k5A9jV68bvt06roCXZAsbpdFJZWUlZWdm03jyVZmkenoshAtG4wlvdbkLOfmrshanvt7+/H4PBkP34fe9TGZc2mbdz3ifSC9OOlKcIjNsmx+/3T6pFzuKKwowcQrvFkF5sYnEk5p8LMY4Zy1ns6OhgZGQklXy7detWABYtWjShkUdCzAehaJzvPbE77drz+5z8a5+Fc1c34HA45kw7mHyJdb+BPhkoJr39CAzuhvIl+VnUIVRVJRwOpwWG4XAYVVXRaDSYzWYKCwuxWCzYn/ttKlAE0Hq70b75OzjtC9QVW7n76uP5zuO76HQG2bi0nEvffQ5YJr6LunnXYMa1R7e2c2y1GbPZjMFgyB5c9b0F2x4Esw3WfAAKpxdcrm8t489be9KurawwTKugRVEUOjs78Xq91NbWjjvxZDKuWt/Eg691pYod9FoNn9qQvVflRG3rdvPRX71CnyeEBrjs2GpubWwkEAjg9XrHPzIvbsq4pCluTvs8madYXl4+bp5isk1OXV1dWlCeLNyZTIscjUbDz686jpsf2c7LB0ZYVm3jK+9enrcWYWJ+mrGflq997Wv86lejxy/HHHMMAM888wwbNmyYqYcVYla5AlG84cyKPNVSQmlpRkvteSEaVxj2RagoMqHVTmzHR1VVotFoqqPB2A9z7xs0Z/uioDPb1RmXXOvYwDAUCqEoid1Ak8mExWKhuDhRzGE2m9FqtcTjcbxeL6q7J/NOPaNHoScvKuPkRVNoinxQQ4mVHb3pldjFhnhq+ohOp8NsNqfWZrFYMLY9jeYPH0g0VQbY8mP4+D/BPvVpKpeurWNrl4v7X+4kpqisrjTz2Q1NUy5oSbZ4CYfDOalQTmouK+DvnzmVP77SRTAa58I1Nayomd7x55cfeivVPkkF7n+tl02ramk0+hJvGMY5+o2tvIzYCz/F7Dr4BlJnhLO+nvrzaDSaylNUVZVAIEBLS0tanmIkEqGnpwe73Y5jzOST6bTIaSwt4J4PnzDh2wtxqBkLFu+55x7psSgWvCq7mWVVRWm5XTqthtOWzM90jb+/1cvXHt7OkC9MQ4mV715+NMc1jQYHiqIQiUSyBoXJGbAajSaVf1xYWIip8l2or98ymkAPiWKOuuNm5XuKxWKpwDAZHCZHCCYnxZSXl2OxWLBYLGk7wYqi4PV6cbvdiUBRVWmo34htzwPpD7L8PTlb7xc3LeXjv36VSDwRvC6rKuK6d63FrINgMJg6Gne73QwNJY6rW5/+JpYxu534B+CVX8CZX5vyOp7bO0QkpnD52lqOLVNYU1tES8sU+viRCIDa2tpSx6rTnnxziLpiK587Oze71HFF5c0ud8b1F/f2U9GszTo9BQ4erw958J/1CxYru9EHR2DpJnA0pP68qysxXnRsnuLY4pRkLqNOp6OmpiZ1faItcoSYKbIPLcQ0/fD9x/L5P77BG50uKm0m/uvdR01obNpcM+QL89k/bE0FKR0jAa797as89JGVxKOJADESGZ3IotPpUrtwDocjFSBmPSb90EPwjy8nClzqjoNz/xe0uX/BUxQlIzCMRqOp9VosFkpKSlKBYbZqdEVR8Pl8qQBRURQsFguVlZXYbDaMi38Afzcm5nRbiuHU/4TWM3L2PWxYWsHT/3k6T+7op6TQxLkrKlMV0QaDIW38XSwWIxQKYYy4Mu/INzDlNfzxlU6+8Kc3U58/YtTy8HUtUypoCQaDtLe3o9VqaWlpmfNFjDqtJuMNIEC1KUpRUdm4R/BOp/NgB49G9PbVGX8+MDCQlqdYVFSUkXOYrU3OZFrkCDFTJFgUYpoWVRTy8HUn4w1FKTDqJ3x0O9f8+8BIKlBMGvRFeLN9kKOqbRQVFaUCQpPJNLmRdxXL4EMP5nS9qqqmFaAkd90gsbuZnC2dDAyNRuO4u2LJSTputxuPx4OiKJjNZsrKyrDb7YcEOEa4+CeJjxlSV2zl6pOzHt6n0ev1iRzwVZfAlh+m/+FRF0758X/67P60z30RhQde7+WLmyZ3vOvz+ejo6MBkMk15JnM+/M9FK/nor1/BFUi80di0vJS11casDbhhdMJKcXFx1iNqn8/H4OBgKk9Rq9VSW1ub9vMYCASytsmZaIscIWbS/PiXK8Q8UDTLowJzrbksc8fEpNey/uhlOKz53c1QVZVIJJIWGAaDwdTRdzJ3L7lraDabj3hcqqoqfr8ft9tNsOdtrN3Po7HVULr83diL51n1+hlfhWgwMbrNZINTPguLz57y3fmz5OFmu3Y4LpeL7u5uCgoKqK+vn1dHp8c1lbDlxjN56cAw5YUGtJ4+bDZb1p+JZNGO0WjMmLACiTzF5NxnRVGy5inG4/HUbOexHUdcLteEW+QIMZMkWBRCALC82sYVx9fzh5c7U9c+e9aSvASKYwtQkh9j8wyT84mTu4YTPR5NFhUkdxBjsRglvf+k9YWvjVY4tz0IVz48U9/azDCY4T3fTXzkwEXH1PLjf47O4tVq4MJjxi+WUVWVu59v44HXurAYdFx2dBkrbBEcDkfGDtp8oCgq33tyN799sR1FUTlnUSG3XpG9h3B/fz/hcJiWlsxj+mQOokajSeUpVlVVZewQZmuT4/f7U1NyJtIiR4iZJMGiECLl2+9dzaVr63i7z8vxTcUsq7Id+YumKdnoeuzH2DxDq9VKaWlpKjCc7FGmqqqpghC3200sFkOv12O327HbbFgef19aKxw6Xki09ll1aS6/zXnlhrOXoNdp+csbPdgtBj55euthx7X98vk2/ntMr9FX253c8d7FvHvF/AsUAX69pS3tKP6RnR5WvNTFJ05vTbud1+tleHiYqqqqrEU7AwMDqZnSPT09FBUVZXRJyNYmZyotcoSYSRIsCiHSHNdUklYBnUuHNroOBoOEw2EAtFotZrMZu92eVoAylRfKZD5jMkCMRqPodLpEgGi3j87ijoXB05V5ByMHMq+9g+h1Wm44ewk3TLDC+E+vpj+HKvD0/gDvOX5+BjlPvp1ZHPTEjv60YDEWi9Hd3U1hYWHWNllerzeVgzg0NJQ1TzFbm5xDW+RMdUqOELkkwaIQYtL2DfoY9IY5tqEYoz77i1kyzzAQCKQVoCQbXZtMJgoKCigrK8NisWAymaa9gzI2QIxEIuh0Omw2G3a7nYKCgrT7DwaD9PX1UVF2DAVDr6ffUQ6rm98JTFl+BszG+ZOjeKgqe2Zu4thryQplVVWzHrMn+ykWFhamds4PzVNMttIZ2yZHWuSIuUqCRSHEhMUVlRvu38rDByd7VBSZ+OXVx7OixkYsFksLDIPBYKrRtdFoxGq14nA40hpdT4aqqvzgqb38eksbMUXliuPr+eKmZcSikVQOYigUQqvVYrPZqK6uprCwMOOFPBwO09/fj8fjwWQyoVz4Q9THPoOm++BIvg03Qd3a3Dxhsy0wAq//Brz9id6Pjetn5WGvOaWZT/9+NOA26rV84MSGWXnsmfCJ01p4fHtfaipMoUmfNhVmZGQEr9dLY2NjRvulsXmKDodj3DzFwcFBAoEAzc3N6HQ6aZEj5jSNmiwnnIM8Hg92ux23253WW0wIkR9/fbOH6+9N34VbVWXltk3VxGIHx63p9VgsFqxWa9ZG11N138sdfOmBt9KuffyEci5YkjhSTu4gFhYWZg1Eo9Eog4ODjIyMoNfrqaysxOFwjAaT/iEwFYF+bvcBHFfQCXedDq720Wvn/3+w9upZefjNuwd54NUurEYdHzypkZW187t6d8AT4uGtPSiqyoVralM7i6FQiH379lFcXJzWODupr6+PoaGhVJ6i1WrNmLgSCATYv38/5eXlqXY8AwMDDAwMUF9fL5XPYtZMNM6SnUUhxIRlm2zx9kAgNRpvvEbXufDotr6Ma/9q93HdmUspKioad6cyHo8zNDSUyhurrKyktLQ08/YF87zi9I370gNFgM3/N2vB4ulLyjl9nk4uyqbCZuZjp6VXQI9tk1NVVZXxNV6vl6GhocPmKSbb5FgsFioqEvO7XS4XAwMDVFRUSKAo5iQJFoUQE7a6LvOF7Oj64nGbFedSeWHmjl9tqW3cF1dFURgZGWFwcBBFUSgtLaW8vHx288Cc7dD2HJQugoaTZvShVP8gGRmf/qEZfcyJiCsqv/jXfh7d1kdZoYlrNxy+snou6+vrIxKJ0NramvFm49A8xVAoRHNzc0b1fm9vb1qbnLEtcsb2WBRiLpFgcYbt6PHw02f3MegLs2lFFR88qVHaIIh567yV1Vy4pj8tZ/EbF6yYlcf+2GktPLatD+/B5tBmg5ZrN7Rm3E5V1dROTTQapbi4mIqKihnb8RzX67+DR64H9eBUnJWXwqW/mJGHikajDDqOoxotGsZM4Vlx0Yw83mTc/vgu7hzTs/HZ3YM89tnTsjaBn8s8Hg8jIyNUV1dnNOcem6dot9vp7u7OmqfocrlwuVzU1tZiNBqlRY6YNyRncQZ1OQOc+71n8UdGe7h9+oxFfP6cpXlclRDTN5Fq6JnQ7Qry4KtdxBSVi4+ppWlMwKGqKl6vN9Uk2WazUVlZmZ9ZxLEwfGdpIo9wrA8/mvOiE4/HQ3d3NxqNhkbfa1he/D54+xIFLpu+Deb8/u485puP4zw4Ni/pP85cPOG2PHNBNBpl7969WfMPYWJ5ipFIhL1791JUVERdXR3xeJz9+xO9HKXyWeSL5CzOAQ++1p0WKEKi2es1J1RiMBjQ6/UYDAbpoyXmndbyQlrLC2f9cWsdFj595uKM636/n/7+fgKBAAUFBdTW1uZ3jq5/MDNQBBjclbNgUVEU+vr6GBkZoaioiNraWvT6ZXDc+3Ny/7miyzIrXT+P5qcnW9xoNJqsbXKy5SnW1dWl3e7QNjmqqqZa5LS0tEigKOY8CRZnULY923hcoasrvYGtTqdLBY7J/479f71ej16vlyMKIQ4RCoXo7+/H6/ViNptpbGzM2i5ntqlFNcTtTejdbWOuaqDp1JzcfzAYpKuri0gkQnV1NSUlJaPfs28QOrZA2WKoWJ6Tx5uOK9c18d0ndqc+LzTpueTY8UcHzjXDw8P4/X6ampoy8g8jkQhdXV0UFRWl5SkeGvyNbZOj1WpTLXKamprys/MtxCRJsDiDLjm2lrue3UdgzO7ileubWb58MbFYjGg0SjQaTf1/LBYjHA7j8/lSbUjGOjSAzBZUyjtU8U4QiUQYGBjA5XJhMBioq6vDbrfnPUiExC7SwOAg3rVfofmVb6DzdILJBmfdDGWLjnwHR7jv4eFh+vv7MZlMtLa2pufPbXsQHvoExCOJz4//KLz7O9N6zOm6fmMrBN280BGgrtzOx05toa44j7u+kxAMBunv76e0tJTCwvSd9GSeYrKv53h5ioFAgIGBAcrLyykoKEj93NbV1VFQML/yNsU7l+QszrBt3W7u3LyPQW+iwOXq9U1oJ3AEo6oqsVhs3KAy+d94PP2YW6vVTiionAsvqvk24Alx9wttdDmDbFxazsXHzM85tu8ksVgs1StRq9VSUVFBcXHxnEnlUFWV/v5+hoaGqKqqoqykBFxtUFgFxukFSMlqW7/fT2lpKZWVlenfdywC310OgUMqoD/6dF6bjAeDQfbt20djYyNFRUV5W8dkKYrC3r170Wq1tLS0ZPyMjc1TTI79q6+vz2iTs3fvXvR6PS0tLbjdbrq6uqioqEi1zREinyRncY5YWWvnR+8/dtJfp9FoUkFetgH1SYqiZA0ko9EokUgEv99PLBbj0PcEhwaT2YJKrVY7+eApMAJv/QliQVhxMTjm5hQHbyjKxT9+gW5XEIC/vNHDngEfX9q0LM8rE9koipLqlQhQXl5OaWnpnNpJV1WVvr4+hoeHqa6uHp0XXNJy+C+cgLQilvGCLl9fZqAI0P9WXoNFt9uNTqfL2Jmb63p7e4lGoyxatCgjUPR4PAwNDVFZWcnQ0BA6nS5rPmOyTU5TUxOBQEBa5Ih5S4LFeU6r1WIymQ6b96KqKvF4PCOYTP5/IBAgGo1m7FKODVjHCyr1ev3oL1JXJ/z8TPD1Jz7/57fhyoeh/oSZ+van7O9v9aYCxaR7nj/AJ06uo8Bskt3XOUJV1VSvxHg8TklJCeXl5Rm5Y/mmqiq9vb2p1iqpQHGaFEWht7cXp9M5pogl83uPx+MMBnSUWCsxBvrT/7B+Zvs7Hk6yjdFcSRGYKLfbjdPppKamJuN3ayQSobu7m6KiIqLR6Lh5im63O9UmB5AWOWJem1u/ccWM0Gg0qcDucBRFyXrUnQwug8Eg0Wg0Y5dSp9NhMBioeP372HxjXqiiAdh8K3zwgZn4tqYlcEiVOkA4prBv335Mem3qOTMYDBiNxlSAnPwwGo2HP/qM+OHJb8CuR8FWAxtuhNaNM/gdLSyqquJ2uxkYGCASieBwOKioqJiT83JVVaWnpycVXJSUlOTkfoPBIJ2dnUSjUWpqaiguLs4IMpLPU19fH/F4HNPZ38Hw5OfQ+AdBZ4KNX4aK/O2WBwIBYrHYvJpKEolE6OnpwWazUVyc3jw8OcFFq9Vit9vp6uqiuro6I08xGVAmx08eOHAAnU5HfX39nEmZEGIyJFgUKVqtFqPReNgXZFVVU0ffhwaVOn/mODbc3TO44qk7b2U1//fYLoLR0aDxXauqWLFsCZFIJPX9JY/zsxUdJYPkbAGl+dHPoX3rvsQN3R1w7+XwqRehNLOJNIArEMFmNkwon3Wh8/l89PX1EQqFKCoqoqGhIaMJ8qwJjCRG6FWsAH3mvwtVVenu7k7tIB0aXEzFoUUsixYtynpyEAwG6e3tJRAIYLPZqKqqwmhcAavOhYEdiRQQa24C16lKFiDltY3RJIxtk5NtB7C/v59QKERdXR3d3d3YbLaMNwdj2+RUVVXR2dmZapEz13bEhZgo+ckVk6LRaNDpdOh0uswX8DXvhbYn0q8t3TR7i5uEKruZ3370BL7/5B46RwJsWFrBF85ditmkHzcwUVU1I4hM/r/P5yMajaIoCqhxjtp2yG5qPALbH4LT/jPt8hudLv7zj2+wZ8BHjd3MNy5cydlHzfzovLkoGAzS19eH3+/HYrHQ3Nyc32rR576bSKWIh6GgAi79JTSPtr5JBgVut5u6ujocDse0H3JsEUtZWRkVFRUZO1GxWIz+/n6cTicmk4mmpqb0fEC9EWrWTHst06UoCh6PJ+uO6Fw1NDREIBDI2ibnuR1d3PHUbvxxLesb/Fy83JY1TzHZJqepqYn+/n5pkSMWBAkWRe4cfQWM7IOX7oJYCFZfDqffmO9VjWttYwm/uebECd9eo9Ecduc1lRsaiYCpEEKu9BuY04/i4orKtb99lR53CIAed4jr732NLTedSUnB3DtunSnhcJj+/n48Hg8mk4mGhgaKioryG2D074CnvjH6uX8A/vwp+MwboNWmBYr19fU5OWYdW8SSEQAymr85MDCAqqqZ/RXnGJ/PRzwez0kQPRsCgQD9/f2Ul5dnPPe7epxc87s3icQTKTjb+/yoBgtfWa7LuI9km5xAICAtcsSCIcGiyB2NBs74Cmz4cmIeru6d9eOVlht68mfSgw1bLay6NO32u/u9qUAxKRxTeHH/MO9aVT0bS86raDTKwMAATqcTvV5PbW0tDodjbgQ/nS9lXnN3gKcbxVZLV1cXXq+XhoaGabf1GlvEYrPZqKmpydjV8vv99Pb2EgqFKC4uprKycs4fabrdbkwmU/5SCCYhHo/T2dmJxWLJaGmjKAq/eW5XKlBM+tPrvXzl/FXsH/Rx3yuduANRnC4XwRicukTHCaUxqqsq502wLMThzO3fNmJ+0mqBd3gS96k3QNkS2PX3RIHL8R8FS3o+W7XdjFGnJRJX0q43lMyP/K6pisfjDA4OMjw8jFarpaqqipKSkvwl/vsG4ZlvQee/oXo1bPwyauVKMkLWgnKUgnI6Ozvx+XzU19dPO1A8UhFLJBKhv78ft9uNxWKhtbX1sK205oq4bwiP20lF5fx40zO2xU22PEWUzII4vVbL270e3nvnCxkFc88e8HLhilK+v0pa5IiFQYJFIWbK8vckPsbhsBq5/oxFaaPQLlpTw8ra+VM5OhmKoqTa4CiKQllZGWVlZfnvlXjv5dDzWuL/B7ajdrxI/2V/xdB6CaX7Hkxc15lQzvs/OroTOZXJo/LJ2NPv5f5XOokr8N61tVQYEoGg2WzOKGJJ9pUcHBxM9fCbM7uuh9P3Fjz0SXT921hiLkOz6RYovzzfq8oQjSv85J/7ePLtfkqtOi5oNXL66paMvEKPx8Pw8DBXnNTMwzvfwhseLXK7en0jdz9/IGtnBYC/7xzhv8MxbGbDjH4vQswGCRaFyKP/OHMxpy8p58k3DlBXqOXy01fne0k5l+y1NzAwQDQapbi4mIqKCgyGOfAi2r99NFA8SOM8QPDtJ9CfdxsoX4LhPSh1J9I+5Cfg96fmT0/Gm10uLvvJFsKxxC7yr7cc4H/OqmTDUXVpRSyqquL1eunt7SUWi1FaWkp5eXn+A+qJUFW4/6pE3jJgCA3BI9dC88lgn1uzoP/7rzv49Zb21OdbDmh5cvVyxu79J+c+22w26uurefBTRfz8uQMM+sJsWlnF5cfV8/FfvzLuY0TjKpGYMu6fCzGfSLAoRJ4dXe+gztpAX1+W1kPzWDLw6e/vJxwOY7PZ5kxVqKqqBINBvEMustWeF5dX4ygrA8pQypbQ3t5OIBCYUqAI8PPnDqQCRYCYAv9oi3HFGVWpa+FwmN7eXnw+H4WFhXPmuZow54FUoJiixODAZljz/vysKQtFUbn/lc60a8Gowl/f7OUTp7cevE2in+LYySyLK4u49dL0N3PnH13D4zsOaYJ+0Mal5ZQVzqO/PyEOQ4JFIeYAs9mMqqqEw+F5URBwJH6/n/7+fgKBAAUFBdTV1c2JXLt4PI7L5cLpdBIKhdDrS3E0nIap49nUbaLlK3GsOjd1+/b2dkKhEE1NTVOuanUHoxnX/BE19RgDAwMMDw9jMBjmRjX4VBRUgKEAov7068XN+VnPYeiyPLe6MT1Ok30+W1paDrure/7RNQz7wtzzQhv+SJwikx5VVTllcTn/ee7SGVm7EPkgwaIQc0AyQAyFQvM6WAyFQvT39+P1ejGbzVlbwMy25C7iyMgIbrcbVVUpKiqisrKSwsJCNC334XvqdpSOF9HVHkPBmf8JGk1GoDidxtIXHF3D5t2Dadfes7oap9NJf38/8XiciooKysrK5u+ED1MhbLwJHv/K6LVl74HGdTP2kG/3erj3pQ4iMYVLj6vj+KYjNyHXajV8aF0TP9k8ugtqtxjY3eflpP99ilKrnkuWWbjo+IkVE119cjNXnzz3AmIhckmjHjq7bQ7xeDzY7Xbcbve0qw6FmOt27dqFzWajunp+VJCOFYlEGBgYwOVyYTQaqaysxGaz5XV3LLmLODIyQjgcxmAwUFxcTHFxcVq+5ODgIP39/VRUVKTapsTjcdra2giHw9MOFJN+8a8D/GZLG3FV5bJjqnlXs4FQKITdbqeqqmpu5HDmQu+b0PYclC2FRWcmWmrNgG3dbt575wup432tBn525XGcufzITe0VReXef3fw5Nv9VNvNuANR/r5tNA1Ep4G//scpLK9emMVmQiRNNM6SnUUh5giLxUIoFDryDeeQWCzG4OAgIyMj6HS6vDeKVlWVQCCA0+lM7SImR+EVFhZmnbZxaKAYi8Voa2sjGo3S3Nycs+Pza05p5qqT6unr68PlcgGG/E+pmQnVqxMfM+xXL7Sl5YEqaiI3dCLBolar4YMnNfLBkxoBWP7Vx9L+PK7C39/qk2BRiIMkWBRijjCbzQwPD6Oq6pzPV4vH4wwPDzM0NARAeXk5paWleavajcViqVzE5C5iRUUFDocjbcdOVVXCMQWzQcfQ0FBqYkd5eXnqfpKBYlNTU84CxeS854GBATQaTd6D6oUgW8safySW5ZZHZrPo0+bEA9LyRogxJFgUYo4wm83E43FisdicPZJUFAWn08ng4CDxeJySkhLKy8vzMk0kuYs4MjKCx+MBoKioiOrqagoKCjICsUff6uV//vY23a4gR9cW8qm1No5uqaaiogKNRkMsFuPAgQPEYjGam5tzljvq8/no7e0lHA5TUlJCRUXFnJ++Mh98rGInlxvuRIvC7+Nn8HflJC4+Zmotej61YRE3P7I99XmlzcQlx86tdj9C5JP8xhJijhhb5JLvYDEUjfODp/bw9M4Bah0WPn3GIppsGvr7+4lGozgcDioqKsadkz2TkruIIyMjRCIRjEYjFRUVFBcXjxuEdbuCfPr3rxNTEinab3T7+E4kzj/WrUGj0RCNRmlrayMej9PSktmceSoikQh9fX14PB6sVuu8mb4yL+z+B2uevxYObmSfqtvGUytqOWP9u6Z0d1etb6KprIDHtvVRUWTiAyc2UCptb4RIkWBRiDnCYDCg1WoJBoOTng6Sa1/58zb+9GoXADv7vLywb5A7z6+hubKYxsbGWa/YVlUVv9+P0+lM7SIm5yhn20U81LO7B1OBYtLuwSD9njClVh0HDhxAURSam5unHSgqisLg4CBDQ0PodDrq6uqw2+1y5JxLr/4q49KZgb+D5pNTvsvTl5Rz+hIZzydENhIsCjFHaDQazGZz3otcIjGFh7d2p10LRlV2eM1sOKFxVtcSi8VwOp04nU4ikQgmk4nKykocDsekjnJrHJk7eoUmPVa9yv79+wGmHSiqqorH46Gvr2/+TV+Zb7IF3pp52nJIiHlAgkUh5hCLxYLX683rGrQaMOi0ROPpCf9FBbNzhKqqKj6fL7WLqNFosNls1NbWYrVap7RDd+qiMk5eVMrze4dT167b0ExvVweQCBSnc6QeCoXo7e3F7/dTVFREVVXV/Jq+Mt8cfw3s/BswZrf4+I/mbTlCLHQSLAoxhyQrohVFyVtzZr1Oy4fWNXLX5v2pa+VFJs5fPbP9H6PRaGoXMRqNYjKZqK6uxm63T7sgRKvV8KsPn8DjO/rZP+jjhEY79pgTjUZDU1PTlAPFsdNXjEYjjY2NeU8heEdoPQM++AC88ktQ4rD2ali6Kd+rmvdUVeXF/SMMeEOcurickoLZz0kWc5MEi0Lk0sj+xAtY0AWrLoOW0yf15WOLXHLRCHqqbty0jJayAp56e4Aah4WPntqMwzq9F44+d4i/vNGDTqvhgjU1lBWaUruIIyMjeL1eNBoNdrudkpISLBZLTvP89Dot71pVTTgc5sCBA2i0Wpqbm6dUTKSqamr6iqqqVFZWUlpaOn+nr8xHi85MfIiciMYVPnLPyzy3J9EOy2LQ8bMrj+OUxWV5XpmYC2SCixC5MnIA7jodwu7RaxffBUdfMeG7UBSFt998ldpiM47GVTOwyPzY1u3mip++iC+c6INXbDXws/cto4gg0WgUs9lMcXExDodjRnP8QqEQbW1t6HQ6mpqaphQoBgIBenp6CIVCOBwOKisr8169LsR0Pby1m8/8YWvatSWVhTz+ucm94RXzi0xwEWK2vXpPeqAI8PwPJhUsal/4Acv/+W20sSBUrIDLfwVli3O7zjz44dN7U4EigDMQ5RfPt/GVc1spLi7O+S5iNqFQiAMHDqDX62lubp700XY0GqW/vx+Xy4XZbF6Y01fEO9bu/sxc6T0DvjysRMxFcmYiRK6EsxSmZLs2ns6X4cmbE4EiwMB2+PO1uVlbnvW6gxnXApimVbQyGcFgkAMHDmAwGCYdKCZb4ezZswev10tNTQ2tra0SKIoF5cTm0oxrJzSV5GElYi6SYFGIXFl1GSqHBD2rL5v41x/YnHmt62WIBKa3rjkg27zes46qmpXHDgaDtLW1YTAYaGpqmlSg6PV62bt3L/39/TgcDpYsWSJj+sSCdNqScq5ZX4/+YFSwpLKQWy5ZOKkwYnrkGFqIHInWHEffuv+mcs/vMcYDiQKX07808TsoW5J5zd4Ahvk/9eOTp7fS7wnxp1e70Gk1fOikRj5wQsOMP24gEKCtrQ2TyURTU9OE8yHD4TB9fX14vV4KCgpoaGiY9Ubk81rIndhVt9fleyViEq4+ppjzmg2UVNXTUl6Y7+WIOUQKXITIkc7OTnw+H0uWLJlakUY8BvdeDvueSnyuNcBld8Py83O70DyKxRU0Gg067czvzPn9ftrb2zGbzTQ2Nk7o7yQejzM0NMTQ0BB6vZ6qqipsNpvsJE7G41+Bl+6CeATqjofLfw22mnyvShxBPB5n586dlJeXU1FRke/liFkiBS5CzCK/34/b7aampmbq1bw6faJ33IHN4OpMtAVZYC+yet3sZL5MNlBUVRW3201fXx/xeJyysjLKy8ulFc5kvf0XeOGO0c+7Xoa/fwGu+F3+1iQmxOPxoKoqDocj30sRc5AEi0JMk6qq9Pb2ptq/TItGAy0bDn+bsA86XwRH44KolM41n89He3s7VquVxsbGIwZ8wWCQ3t5eAoEANpuNqqqqaU1zeUc78GzGJWX/ZrxuNwUFBdNuri5mjsvlwmq1ys++yEr+5QoxTU6nk1AoREtLy8wfV+7fDPd9aLRFz7FXwvk/yD4r9x3I6/XS0dGRyjM8XKAYi8UYGBhgZGQkldNYWCh5WtOSJe82XNRIZ2cnAEajEavVitVqpaCgAKPRiEajIRpX+L/HdvLga92YDTo+dmozV5/cPNurf8eKRqP4/X5qa2vzvRQxR0mwKMQ0xOPxVKXsjE9cUVX46+fSezm+9mtYcQm0bpzZx54HkoFiYWEh9fX14waKqqoyMjLCwMAAqqpSVVVFaWmp5CXmwpr3wxu/h+5XE58bCrBccBtLqpcQCARSHy6XCwCdTofVauW3W0f42Zae1N18/S87qLJb2LRydirm3+lcLldqBrsQ2UiwKMQ0JAOOysrM1jA5F/bCyL7M671b35HBoisQYcu+YaodFlrsWjo7OzMCxRf3D/Pdx3fT5QywYVkFnzm9Ae/IYGr6SlVVlRyN5pKxAK55AvY9Df4hWHwOFJRiJLGrmMyHi8fjBINB/H4/gUCAx3YMZtzV39/qlWBxFqiqisvlwmazzej0JDG/yW9JIaYoFAoxPDw8e+PezDYoWwpDu9IuRyvX8E4bNvfs7kE+8ZtXCUbjAKyvt/Ktd7fQ0NCQ2iHsdgW56pf/JhxTALj3pQ7ae4f45rkNtLS05HX29oKm1cHisw97E51OR2FhYerYv7qkj073SNptSgokd242hEIhwuEwVVUSmIvxSamfEFOQLGoxGo2UlmZOPpgxF9wBBeWJNWi0jCy9gn3xaoLBzAkpC9nNj2xPBYoAL3QG2O03pR0lP7atLxUoJm3pDFBT3yiB4hxz3cZF6Me0U7JbDFy9vil/C3oHcblcqeBdiPHIzqIQU+DxePD7/ROqts2phhPhc9uh53U09jpsBVU429vZv38/9fX174ico1A0zoEhf8b13X1ezl0xujtSZM789WY16metfY+YuNOXlPPI9afw8BvdWAw6Lj+unhrH/G9GP9clj6AdDofk7IrDkmBRiElSFIW+vj4KCwspKiqa/QXoTdBwUuJ/gebmZrq6uujo6KCqqoqysrLZX9MsMht0rKq181a3O+36cYfMsX33qmp++PReOkZGxyV+5JRmDBIszklH1dg4qmbhv9mZS3w+H/F4XHoriiOSYFGISRoaGiIWi9HU1JTvpQCg1Wqpr6+nv7+fvr4+IpEI1dXVC3qn4Nb3ruYTv32FzpEgBp2Gj53awrrW9HSAApOehz61nt+82E6XM8gZyyp416rqPK1YiLnH5XJhMplklKU4Ihn3J8QkRCIR9uzZQ2lp6ZxMCB8ZGaGnp4eioqLDto9ZCBRFZfeAl/JCE6WFpnwvR4h5JTner6KigvLy8nwvR+TJROOshftKIsQM6OvrQ6fTzdlfriUlJTQ2NuL3+9m/fz/RaDTfS5oxWq2GZVU2CRSFmAK32y3j/cSESbAoxAT5fD48Hg+VlZVzuh9ZUVERzc3NxGIx9u/fTygUyveShBBzjMvloqCgYHbafol5T3IWhZiAZKsci8UyL96JWywWWltbaT9YKb0rYOFPW/tRVfjAiY28e7Xk7gnxThWJRAgEAjLeT0zYjO0strW1cc0119Dc3Jx64br55puJRCIz9ZBCzJiRkRHC4fC8KhwxGAw0Nzfzan+Mz/1pB8/vHeaFfcNcd+9rPPpWb76XJ0ROvNo+wkd/9TIX/eh57tq8j7gyZ9Pw5wwZ7ycma8Z2Fnfu3ImiKNx1110sWrSIbdu28bGPfQy/38/tt98+Uw8rRM7FYjEGBgYoLi6ed82cdTodT7dlHkPf++8OzpPKYDHP7Rv08f9+9hKRg83Xt3a6cAWjfGnTsjyvbI6KBlHb/kVwOICt9tg5nU4j5pYZCxY3bdrEpk2bUp+3tLSwa9cu7rzzTgkWxbwyq/OfZ4BOm7kTqs9yTYj55qHXulOBYtJ9L3dKsJhN7xvw2/ei8Q/SCMSaz4AP3Ad6GasojmxWcxbdbjclJSXj/nk4HCYcDqc+93g8s7EsITJs3j3Id5/YTY8zwNpqIzedtwy9fn6m+H7wpEae2jlAskmWRgMfWteY30UJkQN6XeabnmxvjgTw2E3gH0x9qj/wNLx5Hxz7oTwuSswXs1YNvXfvXu644w4+8YlPjHubW265Bbvdnvqor6+freUJkbJ/0MdHf/Uyb3S6GPRFeGyPj+9u7sn3sqZsw9IKfvXhE9i0oopzjqrk7quP54xl83OXdEFRFHjhh/Dzs+DeK6DjxXyvaN5577F1FBjTj1JlpvQ4et/MvNaX5ZoQWUy6KfeNN97IrbfeetjbvP322yxbNnoM0N3dzemnn86GDRv4+c9/Pu7XZdtZrK+vl6bcYlb96Jm93PaPXWnXDDoNO//7PNm1ELnz9P/As7eNfq4zwSefg/Kl+VvTPKOqKk+/8jZ/2jZCRGNi08oqLjtONhmy+s0lsO+p9GuX/BxWX5af9Yg5YaJNuSd9rvb5z3+eq6+++rC3aWlpSf1/T08PGzduZP369fz0pz897NeZTCZMJmmwK/LLZsnsO1Zo0iNxosip136d/nk8DG/8Ac66OT/rmYd8Ph+VFoXbLltDYWFhvpczt533f3DvZTCyH9DA0VfAykvyvSoxT0w6WCwvL5/w9Iru7m42btzI2rVrufvuuxf06DGxcFxwdA0/+ec+ul3B1LVPnt46b1rmiPlB1ejI+InSzs+82HwZHBzEYrFQUFCQ76XMfWWL4PpXoe8NsJaCoyHfKxLzyIz9Zuru7mbDhg00NjZy++23Mzg4mlg7F2fqCpFktxh4+PqTufelDnrdQc5aXsmZyyXHT+ROJBLB03oJZVt/OHrRWAhr3p+/Rc0zfr+fQCBAQ0ODvJGbKK0Wao7J9yrEPDRjweITTzzB3r172bt3L3V1dWl/Nsk0SSFmXVmhif84c3G+lyEWoFAoRFtbG5rlV2KvXYJh99+goAzWXQclzfle3rwxODiIyWSiqKgo30sRYsGbdIHLbJpo4qUQQswHPp+Pjo4OjEYjjY2NMpd3spzt8Nx3iA/sYrhoOcYzvoSjXJrLCzFVM1bgIoQQYvLcbjddXV1YrVYaGhpkesZkRYNw97vA04UOqOBFVIbgfb/N98qEWPCk4kQIIWbY8PAwnZ2d2Gw2GhsbJVCcit2Pgacr7ZLm7b+CbyBPCxLinUN2FoUQYoaoqkp/fz9DQ0OUlZVRWVkpxRhCiHlHdhaFEGIGqKpKd3c3Q0NDVFVVUVVVJYHidCzZBLb0YkmWvwcKK/KzHiHeQWRnUQghciwej9PZ2Ynf76eurg6Hw5HvJc1/Bgt85FF47jswuBuaT4NTPpvvVU1PPAr928DeAAWl+V6NEOOSYFEIIXIoFovR1tZGJBKhsbFRJovkkqMBzv//8r2K3GjfAn+8Cnz9oDPC6V+E076Q71UJkZUcQwshRI6Ew2H27dtHLBajublZAkWRnarCnz+ZCBQB4pHErPC+t/K7LiHGIcGiEELkQCAQYP/+/Wg0GlpaWrBYLPlekpirvH3gbMu83vHirC9FiImQYFEIIabJ6/Vy4MABjEYjLS0tGI3GfC9JzGUF5VCYZext1arZX4sQEyDBohBCTIPT6aS9vZ3CwkKam5vR6yUVXByBTg/vvh1FZxq9tvZqaDgpb0sS4nDkt5oQQkyBqqoMDg4yMDBAcXExNTU10hpHTFio+WwOvOtBGuihoG4lVB6V7yUJMS4JFoUQYpJUVaW3t5eRkREqKiooLy+XQFFMisvlAmsplqXrQSuHfGJuk2BRCCEmQVEUurq68Hg81NTUUFJSku8liXlGVVVcLhd2ux2tBIpiHpBgUQghJigej9Pe3k4wGKShoQGbzZbvJYl5yO/3E4vFpFm7mDckWBRCiAmIRCK0t7eneihardZ8L0nMUy6XC6PRKO2VxLwhwaIQQhxBKBSira0t1UPRZDId+YuEyEJRFDweD2VlZZLnKuYNCRaFEOIQ/Z4QL7eNsKSyiNpCLe3t7RiNRhobGzEYDPlenpjHPB4PiqLIEbSYVyRYFEKIMf74Sic3PfgWMUUF4PylRdywoZ6GhgZ0Ol2eVyfmO5fLhdVqlcbtYl6RMiwhhDgoGInzzb/uSAWKAH/Z5cVvKJZAUUxbNBrF5/PJrqKYdyRYFEKIg3rcQbyhWMb13QO+PKxGLDRutxuNRoPdbs/3UoSYFAkWhRDioIYSK5W29OIVjQaOa5ReimL6XC4XRUVFskst5h0JFoUQ4iCDTsv3Ll9DWWEiYLQYdHz9/BU0lEqbHDE9wWCQUCg0t46gX/8d3HkK3HEc/Ot7oKpH/hrxjiQFLkIIMcb6RWVsuekM9g74qC22YDNL9bOYPpfLhU6no6ioKN9LSdj1KDz8qdHPn/w66Iyw7rq8LUnMXbKzKIQQhzDotCyvtkmgKHJCVVXcbjcOh2PO9FZU37w/8+Ibf5j9hYh5QXYWhRBCiBnk8/nmzHi/WCyG0+nEGIqTUWZjlsIbkZ0Ei0IIMcOc/gj3/ruDLmeQM5ZVcPZRlflekphFLpcLk8mE2Wye8cfqc4f4yxs9aDRwwZoaKorMqKqKz+fD6XTi8XjQaDSUrr4SW/s/0MRCiS/UaGHd9TO+PjE/SbAohBAzyB+OcfGPn6dtOADA7//dwX+es4Trz1ic55WJ2RCPx/F4PFRUVMz4EfSOHg/vu2sL3nCi/dMdT+/hZ+9bhl0TIhqNYjKZqKqqwuFwoNevgOrN8OrdEAvB0e+HhhNndH1i/pJgUQghZtDf3uxNBYpJd23exzXrGzCbjHMmh03MDI/Hg6qqs9Jb8cf/3JsKFAHcwRg/e66Nm89rpaSkBIvFkv7zVrEMzrt1xtcl5j8JFoUQYga5g9GMa/5InB07d2E26DAajRiNRkwmU+r/jUYjBoNBAskFwOVyUVBQMCvj/XrdoYxrAUzU1dXN+GOLhU2CRSGEmEGbVlZx2+O7iMSU1LUzl5WzuKWJSCSS+vB4PEQikdRtNBoNBoNh3EBSqz1MMwtXB2z5ceK/S86BY66Ew91ezIhIJILf76e2tnZWHu+s5ZW82u5Muyb5sSIXJFgUQogZVF9i5ZdXHc/tj++i2xVk49Jy/uvdR2GzZLblUVU1LYBMfvh8PiKRCOqYpsnjBZLGeADtz88GX1/ihrv+BsN74Zz/ma1vWRzkcrnQaDTYbLZZebyPndpMnzvIfa90otVoeP8JDVy5rmlWHlssbBpVnbst2z0eD3a7HbfbPWv/2IQQYi5SVZVoNJo1mAyHw6lAsnjfQ9S+fnv6FxuscGMH6KRv5GxRVZU9e/ZgsVior6+f1ceOKyoaQKuVNAZxeBONs2RnUQgh5gGNRpPaPTyUqqrEYjEikQiagSyjCeNRUOISLM6iYDBIJBKhurp61h9bJ0GiyDFJYhFCiHkumd9YUFCA9bj3g/GQkXKrLgPDzPf4E6NcLhd6vZ7CwsJ8L0WIaZOdRSGEWEhs1XD1X2Dz/yUKXBafA6d/Md+rekdRFAW3201xcbFUtIsFQYJFIYRYaGqOgf/3+3yv4h3L5/MRj8fnxHg/IXJBjqGFEEKIHHK5XJjN5lkZ7yfEbJBgUQghhMiRWCyG1+uVXUWxoEiwKIQQQuTIbI73E2K2SLAohBBC5IjL5aKwsBCDQdoUiYVDgkUhhBAiB8LhMIFAQI6gxYIjwaIQQgiRAy6XC61WKxPHxIIjwaIQQggxTaqq4nK5sNlsaLXy0ioWFvmJFkIIIaYpEAgQjUYpLi7O91KEyDkJFoUQQohpcrlcGAwGrNYss7mFmOckWBRCCCGmITnez+FwyHg/sSBJsCiEEEJMg9frRVEUqYIWC5YEi0IIIcQ0uFwuLBYLJpMp30sRYkZIsCiEEEJMkYz3E+8EEiwKIYQQU+R2u9FoNDLeTyxoEiwKIYQQU+R0OiksLESv1+d7KULMGAkWhRBCiCkIhUKEQiE5ghYLngSLQgghxBS4XC50Oh1FRUX5XooQM0qCRSGEEGKSkuP97Ha7jPcTC578hAshhBCT5Pf7icVicgQt3hEkI1cIIYSYoH8fGOFHz+yle8TLunorX10mvRXFwifBohBCCDEBB4b8fPAXLxGJKQDsHQqht+7k5vNX5HllQswsOYYWQgghJuDhrd2pQDHp/pc787QaIWaPBItCCCHEBJj0usxrhsxrQiw0EiwKIYQQE3DJsbU4rIa0a9ec0pyn1QgxeyRnUQghhJiASpuZP3/qZH75/AEGPGHOXVnJxcfU5XtZQsy4GQ0WL7jgArZu3crAwADFxcWcddZZ3HrrrdTU1MzkwwohhBAzoqmsgG9euDLfyxBiVs3oMfTGjRu5//772bVrFw888AD79u3j0ksvncmHFEIIIYQQOaRRVVWdrQd75JFHuOiiiwiHwxgMhiPe3uPxYLfbcbvd2Gy2WVihEEIIIcQ7w0TjrFnLWRwZGeF3v/sd69evHzdQDIfDhMPh1Ocej2e2lieEEEIIIbKY8WroL33pSxQUFFBaWkpHRwcPP/zwuLe95ZZbsNvtqY/6+vqZXp4QQgghhDiMSQeLN954IxqN5rAfO3fuTN3+C1/4Aq+//jqPP/44Op2OK6+8kvFOvm+66Sbcbnfqo7NTmp0KIYQQQuTTpHMWBwcHGR4ePuxtWlpaMBqNGde7urqor6/nhRdeYN26dUd8LMlZFEIIIYSYGTOWs1heXk55efmUFqUoiTFJY/MShRBCCCHE3DVjBS4vvfQSL7/8MqeccgrFxcXs27ePr371q7S2tk5oV1EIIYQQQuTfjBW4WK1WHnzwQc4880yWLl3KNddcw+rVq9m8eTMmk2mmHlYIIYQQQuTQjO0srlq1iqeffnqm7l4IIYQQQsyCGW+dI4QQQggh5i8JFoUQQgghxLgkWBRCCCGEEOOSYFEIIYQQQoxr1mZDT0WyX7jMiBZCCCGEyK1kfHWk+SxzOlj0er0AMiNaCCGEEGKGeL1e7Hb7uH8+6XF/s0lRFHp6eigqKkKj0eR7OUAiCq+vr6ezs1NGEM4wea5njzzXs0ee69kjz/Xsked6duXq+VZVFa/XS01NDVrt+JmJc3pnUavVUldXl+9lZGWz2eQfxCyR53r2yHM9e+S5nj3yXM8eea5nVy6e78PtKCZJgYsQQgghhBiXBItCCCGEEGJcEixOkslk4uabb5b51rNAnuvZI8/17JHnevbIcz175LmeXbP9fM/pAhchhBBCCJFfsrMohBBCCCHGJcGiEEIIIYQYlwSLQgghhBBiXBIsCiGEEEKIcUmwKIQQQgghxiXB4jRdcMEFNDQ0YDabqa6u5kMf+hA9PT35XtaC09bWxjXXXENzczMWi4XW1lZuvvlmIpFIvpe2IH3rW99i/fr1WK1WHA5HvpezoPzoRz+iqakJs9nMiSeeyL///e98L2lBevbZZzn//POpqalBo9Hw5z//Od9LWpBuueUWjj/+eIqKiqioqOCiiy5i165d+V7WgnTnnXeyevXq1NSWdevW8eijj87KY0uwOE0bN27k/vvvZ9euXTzwwAPs27ePSy+9NN/LWnB27tyJoijcddddbN++ne9973v85Cc/4ctf/nK+l7YgRSIRLrvsMq699tp8L2VBue+++7jhhhu4+eabee211zj66KM599xzGRgYyPfSFhy/38/RRx/Nj370o3wvZUHbvHkz1113HS+++CJPPPEE0WiUc845B7/fn++lLTh1dXV8+9vf5tVXX+WVV17hjDPO4MILL2T79u0z/tjSZzHHHnnkES666CLC4TAGgyHfy1nQbrvtNu68807279+f76UsWPfccw+f/exncblc+V7KgnDiiSdy/PHH88Mf/hAARVGor6/n05/+NDfeeGOeV7dwaTQaHnroIS666KJ8L2XBGxwcpKKigs2bN3PaaaflezkLXklJCbfddhvXXHPNjD6O7Czm0MjICL/73e9Yv369BIqzwO12U1JSku9lCDEhkUiEV199lbPOOit1TavVctZZZ7Fly5Y8rkyI3HG73QDyu3mGxeNx/vCHP+D3+1m3bt2MP54EiznwpS99iYKCAkpLS+no6ODhhx/O95IWvL1793LHHXfwiU98It9LEWJChoaGiMfjVFZWpl2vrKykr68vT6sSIncUReGzn/0sJ598MitXrsz3chakt956i8LCQkwmE5/85Cd56KGHOOqoo2b8cSVYzOLGG29Eo9Ec9mPnzp2p23/hC1/g9ddf5/HHH0en03HllVcip/sTM9nnGqC7u5tNmzZx2WWX8bGPfSxPK59/pvJcCyHERF133XVs27aNP/zhD/leyoK1dOlStm7dyksvvcS1117LVVddxY4dO2b8cSVnMYvBwUGGh4cPe5uWlhaMRmPG9a6uLurr63nhhRdmZWt4vpvsc93T08OGDRs46aSTuOeee9Bq5f3ORE3l51pyFnMnEolgtVr505/+lJY7d9VVV+FyueREYgZJzuLMu/7663n44Yd59tlnaW5uzvdy3jHOOussWltbueuuu2b0cfQzeu/zVHl5OeXl5VP6WkVRAAiHw7lc0oI1mee6u7ubjRs3snbtWu6++24JFCdpOj/XYvqMRiNr167lqaeeSgUtiqLw1FNPcf311+d3cUJMkaqqfPrTn+ahhx7in//8pwSKs0xRlFmJNyRYnIaXXnqJl19+mVNOOYXi4mL27dvHV7/6VVpbW2VXMce6u7vZsGEDjY2N3H777QwODqb+rKqqKo8rW5g6OjoYGRmho6ODeDzO1q1bAVi0aBGFhYX5Xdw8dsMNN3DVVVdx3HHHccIJJ/D9738fv9/Phz/84XwvbcHx+Xzs3bs39fmBAwfYunUrJSUlNDQ05HFlC8t1113Hvffey8MPP0xRUVEq/9Zut2OxWPK8uoXlpptu4rzzzqOhoQGv18u9997LP//5T/7xj3/M/IOrYsrefPNNdePGjWpJSYlqMpnUpqYm9ZOf/KTa1dWV76UtOHfffbcKZP0QuXfVVVdlfa6feeaZfC9t3rvjjjvUhoYG1Wg0qieccIL64osv5ntJC9IzzzyT9Wf4qquuyvfSFpTxfi/ffffd+V7agvORj3xEbWxsVI1Go1peXq6eeeaZ6uOPPz4rjy05i0IIIYQQYlyS9CWEEEIIIcYlwaIQQgghhBiXBItCCCGEEGJcEiwKIYQQQohxSbAohBBCCCHGJcGiEEIIIYQYlwSLQgghhBBiXBIsCiGEEEKIcUmwKIQQQgghxiXBohBCCCGEGJcEi0IIIYQQYlz/P3JQxU16HegJAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import jax\n",
    "import optax\n",
    "from jax import numpy as jnp, random\n",
    "from matplotlib import collections, pyplot as plt, rcParams\n",
    "\n",
    "def get_optimal_transport(x, y):\n",
    "    assert x.ndim == 2\n",
    "    assert x.shape == y.shape\n",
    "    displacements = x[:, None] - y[None, :]\n",
    "    distance_matrix = jnp.linalg.norm(displacements, axis=-1)\n",
    "    i, j = optax.assignment.hungarian_algorithm(distance_matrix)\n",
    "    total_distance = distance_matrix[i, j].sum()\n",
    "    return (i, j), total_distance\n",
    "\n",
    "def main():\n",
    "    num_points = 200\n",
    "    markersize = 16.0\n",
    "    \n",
    "    key = random.key(0)\n",
    "    keys = random.split(key)\n",
    "    x = random.normal(keys[0], (num_points, 2))\n",
    "    y = random.normal(keys[1], (num_points, 2)) + jnp.array([0.2, 0.0])\n",
    "\n",
    "    (i, j), total_distance = get_optimal_transport(x, y)\n",
    "\n",
    "    fig, ax = plt.subplots(constrained_layout=True)\n",
    "    \n",
    "    data = jnp.stack((x[i], y[j]), 1)\n",
    "    lc = collections.LineCollection(data, linewidth=1.0, color=\"lightgrey\", zorder=0, label=\"assignment\")\n",
    "    ax.add_collection(lc)\n",
    "\n",
    "    ax.scatter(*x.T, s=markersize, edgecolor=\"none\", label=\"facility\")\n",
    "    ax.scatter(*y.T, s=markersize, edgecolor=\"none\", label=\"client\")\n",
    "\n",
    "    ax.set(title=f\"Optimal transport distance: {total_distance:g}\")\n",
    "    ax.legend()\n",
    "    plt.show()\n",
    "\n",
    "main()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "773c84c2-fcd9-431a-ae17-3c3404181dbc",
   "metadata": {},
   "source": [
    "This, in turn, can be used to estimate the [Wasserstein distance](https://en.wikipedia.org/wiki/Wasserstein_metric#Higher_dimensions) between two distributions, by sampling a large batch of points from each and then computing the optimal transport cost between those batches.\n",
    "\n",
    "More precisely, if $W_p$ denotes the $p$-Wasserstein distance and $P$ and $Q$ are [empirical distributions](https://en.wikipedia.org/wiki/Empirical_measure) with samples $X$ and $Y$, respectively, then:\n",
    "\n",
    "$$ W_p(P, Q) = \\inf_{\\pi \\in \\text{Sym}(n)} \\left( \\frac{1}{n} \\sum_{i=1}^n \\|X_i - Y_{\\pi(i)}\\|^p \\right)^{1/p} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0a7afdcc-6b92-4b08-8fe9-5927a6888ba2",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
